Hello Katie P and welcome to Toms!
First of all, I want to make something perfectly clear, ANY program AT ALL that has a phone number posted on it SHOULD NOT BE TRUSTED. Reputable companies like Microsoft, Apple, Google, etc, do not scare people into becoming customers.
Now, to get to the issue at hand. These guys that you called are not from the United States, no matter how much they may claim to be, and no, they are not trying to fix anything either. These "companies" will get onto your computer, fill it full of virus's/malware and then say you need to pay $xx.xx in order to fix it. If you pay, they won't remove the problems, but will say the PC is fixed. EVERYONE I have spoken to in the last 5 years that has paid has become emotional because it is ALWAYS a frustrating process. IF you paid them, please call your card-company immediately and cancel that payment, saying that you were coerced into paying; the card company can reverse the payment if it is relatively recent.
Here is what I think happened: they connected to your machine, if not in the foreground then in the background. They were loading things into your computer when some form of error happened, which now makes it not boot properly. It sounds like when the hard drive DOES boot, it won't load your OS completely, and crashes to just a white cursor.
I would say that the easiest way to fix your machine would be to boot into safe mode or a Windows install disk, and then recover your PC to an earlier time using "System Restore". That would be my suggestion, I hope that helps.
- Harrison Whitmarsh
Lincoln Nebraska USA