The light is probably just your imagination- unless the charger is getting old and not functioning well. How old is your battery? You may need to calibrate or replace it.

It's hard to say with these old Titaniums. The battery itself is unlikely to cause a computer to freeze. A computer running on battery power will have trouble coming out of sleep mode if the battery is close to dead, but actual "freezing" of the computer due to a battery is something I haven't experienced.

Titaniums are increasingly becoming flaky, and they do generally have motherboard issues at this stage in the game which cause many of them to randomly freeze. It might be solved by a DC-in replacement, if you want to explore that route.

I would also verify the memory slots by putting RAM in only one slot or the other, and resetting the PMU and PRAM after each change...sometimes this can "jolt" a laptop into working again, and, who knows, you might find that one of the memory slots has a problem, and that the laptop works fine when the bad one is empty. It does happen fairly often.