Sounds like a button/button contact sticking/not releasing. Just the fob is replaceable by swapping the key and chip if it is ou that generation. Need some more information. What year if it's not in your post. It is. '04. You have an immobilizer chip! No problem. I have the How-to to swap the key and chip and sourcing for the fob if you want new, or eBay for used....on another problem...
I have replaced the battery in the key 5-6 times. It works great for a few days then...nuttin' honey.
The first time I thought, "maybe the battery I bought was bad"...the next 4-5? I don't think so.
Anyone else have this problem?