Could not repair the FOB but found a Solution
Well, for anyone interested I purchased two 4-button key fobs with Remote Start from:
remote key fob, keyless remote replacement items in keyless entry remote store on eBay! for about $37.
I was told by that seller that I could program the new fobs with my one OEM fob (that defective fob would work for about one day with a new battery) and my Transponder key (the grey keys that have no remote entry buttons but will crank the truck and manually open the door). I was also told that I would have to have the new key fobs cut in order to program them as they have to be the third unprogrammed key that you place into the ignition to program keys (as when following the programming instructions in the owner's manual).
I did not want to spend money to cut the keys, so I took my OEM fob key, opened it and removed the electronic board, I then took the new fobs apart and removed their electronic boards. Then I held with my fingers the OEM electronic board in place in the OEM fob and used it as the first key (in other words, the key fob was apart and I merely held the board in place while I turned the ignition on), I used my Transponder key as the second key, and then I quickly removed the OEM electron board from the OEM key fob and took the one of the new electronic boards and held it in the OEM fob with my fingers (which had my OEM cut key) and used it for the third key.
By that method I fooled the truck and programmed the new key fobs without cutting them. Since my OEM key fob does not work correctly, I simply placed one of the new fob electronics into it, and it works fine. I took the other new fob, removed the metal key (it merely slips out when the screw is removed....unlike the OEM key), and placed it on a key ring with the grey Transponder key. So now I have two key fobs that work....one with the original OEM key and one on the key ring with the Transponder key (actually I have two transponder keys so I am set with regards to extra keys...).
Thanks again to everyone who offered good advice and help!!