Macbook Air 2012 Mavericks/Yosemite update failure, apple id not recognised

Hi

I seem to have broken my macbook! I had Windows7 on a partition but after a year decided to go back to OS X (was fed up of switching between) and in the (naive) process of unpartitioning, resetting, updating it can no longer recognise my Apple ID (although iCloud, iPhone and iPad mini all recognise it, no problem), won't hold WiFi connection. So I cannot log in to Apple Store on it to download an installer - I've managed to connect via Thunderbolt, but still cannot get into my account on Apple Store whilst on my Mac!

Pleeeease can someone help a (silly) macbook user (me!)

Cheers

T