I would not recommend by-passing the security system. In regards to buying a new key fob, you can find many in ebay. There is a procedure to program your security system to respond to the new key fob. Some of the key fob sellers in ebay will offer you to include the programming procedure. That’s an easy task.
In reagards to the alarm going off when using the key, you will have to check the door locks from the inside an verify all wire connections in the lock.