There are some calculator collector web sites that may be able to help.
If your SR-56 has a nicad pack, chances are that the problem is that the nicads have died. They are normally pretty easy to replace yourself, although you may have to cut open and re-glue the battery pack.
Some of the earlier TI calculators used a pack with a single AA NiCad and a boost regulator using a TL496 to get 9V to power the calculator. If you have one of these, it is possible that the inverter has died.