I started hunting late yesterday (well, more like 2am today) and could not find any online instruction manual (or, indeed, very much about that Acer Aspire One model).
What I did find was some hints about getting 3G working (first check was the switch, second was in the power management settings). So, by working the 'opposite' way round, it might be possible to disable the 3G via the power management, and if not there, via the notebook's system configuration.
However, I am a wee bit worried about trying to 'talk you through' this if you're not used to 'messing about with the settings' IYSWIM.
Where was the notebook bought ? I found something on the UK Acer site about support for units bought through PC World and other parts of Dixons Stores Group (Dixons, Currys) were not supported by Acer.
If the place it was bought from is local, is it possible to visit there (first) ? I'm happy to try to disable the 3G but don't want something nasty to happen and for you to (a) have no usable notebook over the weekend, or (b) even worse, land you with a costly bill to get it sorted out. I'd feel bad, and at present could not offer to repay you any costs for getting it fixed afterwards.
Anyway, another question, in case it's not practical to visit the store, is to ask what version of Windows you have, please? Next I'd ask you to open "My Computer" if you can (if not, can you get the Explorer window to show your documents in 'My Documents' and we will go from there).
Don't want to be over dramatic, but we're getting into system changes that I'd only do with great care on any of my machines, to be able to disable this bit of your notebook. It's not a route I'd go down in a hurry, but clearly this problem is getting in the way of you using your Notebook, so may be the only way...