Its a leap of faith to buy a used car that can't be started, unless its a really good deal
Like most newer cars these days, if the Vibe has the immobilizer system then there would be a transponder in the key, and the car would be programmed to recognize that specific key. That programming is something GM/Toyota never made public, so you'd need to take the car and key to a dealer to get that done, and as andrewclaus said, it can be pricey.
If it is an issue with the immobilizer, then it could be that the new key doesn't have a transponder, or if it does, then the car wasn't programmed to acknowledge that transponder, or it could be a problem with the actual immobilizer system in the car.
There's a little (but likely unhelpful) bit of info on the Vibe immobilizer system in the
2009 Vibe Owner's Manual