Verizon service, AT&T iphone, switching?

Okay, I have prepaid service with Verizon, but I have a AT&T iPhone. I accidently broke my non-smart phone the day before I paid my bill. Someone told me that you can switch your Verizon number over to any Verizon phone, especially if it's not a smart phone. I jumped the gun and went ahead and added money to my account. Turn out I couldn't switch it over because the phone I was going to use isn't compatible. My friend who works in Wal-Mart's electronics told me that I could get a refund at Wal-Mart (since that's where I bought it), despite me scratching the back off and putting the money in my account. Since my aunt gave me her old iPhone, my friend said I could swap the Verizon refill card for an AT&T one. Turns out she didn't know what she was talking about. I called Verizon; because I used a refill card, instead of a debit/credit card, I can't get a refund. I was wondering could I buy a prepaid Verizon sims card (if they exist) and switch my account to that and use it for my iPhone. I don't know a lot about phones and if this is even possible, but it's a theory.

No, AT&T and Verizon iPhones use different types of cellular service… They are not at all compatible.