Ok the first thing I want you to do is force yourself to be open minded to all advice people give you here. As I can tell from what you've written you're only gonna see anything good in this girl. I'm going to deconstruct what you've said and you may naturally see it as an attack, but please don't.
You "can't find the moment to approach her" because you still believe the way dating and romance in the real world works the same as it does in the movies. This is hard to put aside as when we speak to people in relationships, they describe how they met etc, and words are very powerful. People in relationships make some fairytale hollywood description to how they fell for each other. And that is nothing more than delusional. In short, there is no perfect moment.
It's hard to predict other factors based on age, but as you say school I'm guessing mid to late teens. These age range is a very broad spectrum, as dating is very different.
"because over the years of non-stop gaming I've lost my social/girl talking life." - This is lack of self belief and confidence. Notice how its a negative reason you gave yourself to why you cannot try to do something you've not done many times before? If we change your wording here slightly to "social skills" which applies to all social aspects of life, then what does skill mean? Like in video games, activities, sports, studies, and yes social life, skills are something we develop with practice over time, and those who never give up will always develop their skill far beyond than when they first started.
Now as she is only two weeks back in to single life, which means her mind is going to be all over the place with adapting to single life, and also depending on how her previous long term relationship ended.
As she is an attractive girl like you said, and you're in an environment surrounded by lots of males and females your age, she's going to have attracted the attention from lots of other guys. Don't think that from being her secret admirer, that there's not another 10 guys the exact same.
I'd strongly advise not trying to get too close to her now. It's mistake number ONE in nice guy mentality. They are baited by a girls breakup and mood swings, and then be the super nice guy offering support when she cries etc. Nice guys do this to try and make the girl realise "oh wow he is a super nice guy" blah blah blah, hoping the girl will fall for him. In reality it does the exact opposite. It's manipulative behaviour as the nice guy is trying to be too nice just to satisfy his infatuation with a girl, and is often unwilling to accept that the girl may never be attracted to him. The girl will be manipulated to some degree, but it will result in being friendzoned as she sees you as a super perfect nice guy that she wants as a
supportive friend. So i urge you don't do this if you saw this as an opportunity to get really close.
I'd definitely not say you shouldn't try and get social with her though. See this as an opportunity to learn and control your emotions and social confidence with girls. Be civil with her, smile, don't agree to everything she asks (such as favours), and honestly just breathe. Lots of guys around you will try what i explained in the above paragraph, and they will fail miserably. Just take a step back from the crowd, be nice to her if you ever get into conversation. Keep the conversation short and sweet, and don't be afraid to talk to other girls in front of her as that would make her curious. Then if she starts initiating conversation, casually ask her out. Do this earlier than sooner, don't play this safe as rejection earlier on is much better than later on, even though it takes more courage.
This has become a very long reply to your topic lol but as I've been in your exact situation in the past, I felt the need to step in incase you get hurt and lose confidence because of any outcome you don't want from this. Pasted below is a reply I posted on a friendzone topic, which you may also find useful as it will enable you to look at your situations with girls from a different perspective.
-------------------------------------------------------------------------------------------
source:
Friendzoned
"
As someone who got crushed with the friendzone as a nice guy for many years I have a few things to let you think about.
1) If you're speaking to a girl you like who has recently broken out of a relationship, don't be the guy to offer emotional support. Girls love drama and gossip. She will list all the things her ex has done to piss her off. You may see this as an advantage but it's really not. Chances are she will see you as a friend who can give her support and attention 24/7 (just like some of her female friends). She will friendzone you before you even know it, and you'll misread all of her signs as false attraction. Then you will be hurt.
2) Being the nice guy can actually you not being honest to yourself that you're being manipulative. You're going out of your way to give a 10/10 impression, which you wouldn't do with your male friends or any female friends you're not attracted to. This will always result in failure as she has your attention too easily.
3) Don't try girls who have ex's or current boyfriends/flings close by as it's 9/10 times a waste of time as their main focus is on that other guy. If these guys in question are 'getting in the way' they've read you from a mile off and are protecting 'their girl' from you.
4) Keep busy and put your activities and/or studies/career before replying to a girl (if text/online interaction etc). Replying instantly has no game and girls lose interest quickly as they no longer find you mysterious and may even see you as emotionally immature.
------------------------
It is hard to fully understand your situation as there are so many possibilities and there is no magic formula to seduce women. It either happens or it doesn't. Trying to find a magical solution is being the manipulative nice guy who doesn't realise he's being selfish.
I've been there believe me. I've had points in my life where i was acting all fairytale and thought 'she' was the only one. Other times I've been the 'insecure player' who thinks because he's speaking to lots of girls then one will magically jump into bed with him.
Just keep focusing on improving yourself, and not trying to be someone you're not. Develop different areas of your life and you will become a person with diverse interests and fun to be around. Keep trying with girls and accept rejection although it can really hurt sometimes. Trust me, a few months down the line you may even silly for liking a girl so much.
-------------------------
I hope that somewhat makes sense. I could go on forever about my past experiences but to be honest what my conclusions are of my past are just the conclusions i've come to and may be different from you or anyone else.
If you feel a bit lost and unsure where to begin. Do by all means do some online research.But don't sign up to any bullshit courses or communities which claim they have secrets to seducing women. There is none. End of story.
The closest you can get is understand social cues, and actually trying over and over again.
As the cliche goes, practice makes perfect."
