If internal codes don't exist for your item, the only solution is to manually program those buttons. Since you report this as a "Digital" cable box, it's possible GI used different IR codes than on their "Analogue" cable boxes which would be what the AV2000 has built-in.

As for power loss, Sony claims there is a 1-hour backup. I myself have inadvertaintly tested this for at least 8 hours, with no loss of memory.

While programming the original "universal" remote that came with Sony receiver I decided I wanted to completely reset it - so I took the batteries out, left it for an hour, came back and everything was still there. So, I phoned Sony. They said take the batteries out, press every button (to drain any power left in it), and after that it'll be reset. Still didn't work. So, I tried their suggestion but left it without power for the entire weekend. Came back, still hadn't lost it's programming. My final solution was to manually reset every button, which took quite a while.

I don't know if Sony engineered the AV2000 with simular technology - and I really don't want to test - but I wouldn't be overly concerned about losing programmed signals. Once you get the hang of it it only takes a few minutes to restore a single device any ways.