Yay! another person who type thoughts and feelings carefully, not ragged - FO love to read coherent text!
So there is girl you like but girl is holding off any close conversation. Currently, you like the girl and you know that in friend setting, relation works ok and you want more. Problem, half a year ago you no have luck and she leave you in cold. Then she reignite fire but mainly hide behind internet. Correct?
Frigid Onanoko not know ho relation with her looked like exactly, before she cut you off. Also not know how you ask her for more. However, girl sound like wanna be in control of things, and you asking did not fit in her schedule. Perhaps, you in wrong place of her schedule, perhaps you never in her schedule to begin with. Her reinitiating contact show that she felt she overreacted 1 year ago.
Other direction that can think of is that you also did something else, or that you really really messed up somehow back then when or before asking her out.
Everybody know that chatting with boy (girl), with coffee and cake, on the computer, sucks when compared to chatting with boy (girl), with coffee and cake, on a terrace. You want to move to the terrace, but she avoid all terraces with you. Now for the advice.
She closed the door on you. Then she open it again, the little bitch. You wanna write her that she need to step through the door, or you gonna close it for her. It perfectly fair to ask why she keep you behind internet - are you not good enough to be around her? (maybe you not wanna ask so direct). Anyway, she already know you like her. It not unfair to write her letter and tell her that you value her, but that you want to see more of her in real life. Otherwise, it will keep feeling like one of those marriages where the partners have their separate beds, on the opposite sides of the room. Please let FO not have to in explain that part... Hm, this not much advice, really, but then situation is not super clear yet!
Saying good bye now!
p.s. make sure to draw a piano once. Draw it so well that a pianist wanna play it right then and there. (FO love piano)