PATS problem, key code not received and battery light on

I had a dead battery on my 99 Expedition, and replaced it. After replacing the battery, the truck will not start. The theft light flashed rapidly and the battery light came on. The theft light started flashing 1:3 (1 flash followed by 3), which I believe means that the key code was not received. I tried someone's suggestion I found on the forum of disconnecting the battery, waiting for the rapid flashing of the theft indicator to stop, taking the key out, waiting 15 seconds and putting it back in. This did not work, and I still got the key code not received code. Now the theft light does not come on and the battery light is illuminated, even with the key out.

One problem I have is I only have the one key. Can a locksmith reprogram my key and make me a spare with the one I have? Any other suggestions, and why would the battery light stay on with the key removed? Thanks for any help.

Problem fixed

I have it fixed now. The problem was evidently a water leak from the windshield onto the keyless entry module. I got the truck started and took it for a drive. I could hear sizzling coming from under the dash. Upon closer inspection, I could tell the noise was coming from the keyless entry module. I cranked up the heat, closed the truck, and left it running. After a few hours there was no more sizzling sound and everything is now functioning normal. I got the windshield replaced.