Can I buy a new iPhone on a new contract while I have a current contract?

I have an iPhone 4 with a Verizon 2 year contract ongoing, but it suddenly stopped working a day ago. I need a new one and saw that the iPhones alone go for like $500. So I was wondering if I could start a new 2 year contract with Verizon? Would I be able to keep my number and info from my phone's sim card?

Probably. You will have to continue paying for the old phone, though.
Why not see id it can be repaired?

Yes you can, but there's a problem. That means (if they allow it) you will have two, yes two, phone line bills, or worse, 2 contracts, not just one long contract. So you'll have phone line 2 bills, not just one. You could use a tin can and string. They don't care as long as you pay that first phone line bill as you agreed to do. Your next best (and cheaper) option is to shop Ebay for a used Verizion iPhone to replace your broken one. Why do they do that? Because they got wise to getting ripped off is why. People would conveniently 'break' their phones right before the next one comes out and then go extend a 2 year contract to 4. Then the customer would get fed up a year later with the bill and walk leaving the company basically out the cost of two phones. That's the only way to guarantee you keep your number, your credit, some money in your pocket, and current sim card. Best luck.