You might want to start by verifying that the issue really is a difference between the built-in TV/0060 and your TV (and not something wrong with your 2116 or something else strange that we haven't guessed yet).

Learn a signal from the original remote into the 2116 and see if the learned signal works well. Be sure to use a long press of the button on the orriginal remote when learning. If that works well than it is some issue like the one Rob suggested or the one I suggested, either of which can be fixed easily with JP1.

If the learned signal doesn't work well either, then something else is happening. Maybe JP1 would help that too, but maybe not.

You can find the introductory info about JP1 on Rob's site
[Link: hifi-remote.com]
then there are links to the Yahoo group where all the files (and help etc.) are.

Once you're using JP1 you'll need a few learned signals from the orriginal remote to see whether you have what Rob suggested (which my new decoder will display as "NECx2") or a standard "NEC1" or some other form (TV/0060 is what my new decoder calls "NECx1"). Once you know which it is, it is easy to create and load into the 2116 a new setup code that will be an exact match.

(Having read Rob's message, I now think his guess is better than mine, but you need JP1 either way and with JP1 you can find out for sure which it is).