If your dealer can't get one from factory using your vehicle number, - it is going to cost you a "bunch", --- probably about $50 or more to get a locksmith to check and make a new key to fit! Now if yours had the "little electronic button" on it to operate locks (and even worse some require it to make ignition start car!) -- Then you are in real trouble!!
As soon as you get it "fixed" my advice is to have 3 of each kind of key available! One for ignitin (and doors, if different)-- one set in wallet, and one set stored somewhere you can find them in house-- or if married one set with spouse! Now if you loose set,- or lock them inside car, you have a set available quicker and cheaper than if you have to order new ones, or get locksmith! --- this is what I always do!
For our Saturn, they told us it would be $75 when the battery dies
We had one set of keys with remote stolen, to replace the remote and reset them cost us $80.
Wanted to add we replaced the key at a key shop for around $25.
Those "smarter" key fobs, with remote controls and immobilizer anti-theft chips, are stunningly expensive. I think the ones for my Volkswagen run between $150-250 depending on where you get the parts and who does the programming. A quote of $350 sounds a little high to me, but it's not out in the stratosphere. :-(
I went to the local hardware store not knowing their was a chip in the key for my Lincoln Navigator and they told me they could not make the key for me but to bring it to a locksmith. I called the lincoln dealer and they wanted 250 I went to the locksmith and they charged me 75! Try visiting a locksmith because they have the tools to program the key.