I would like to try and restore or rebuild the battery pack for the Game Gear. The old one works but it won't last more than a few seconds after I disconnect the power, the original cells are NiCd which are pretty much garbage. I was wondering if I could just straight up replace them with something else of newer technology like rechargeable lithium or if the charger would have to be redesigned? NiCd generally have poor life compared to other types such as memory effect. Plus newer types have higher capacity and longer use time.
You should be able to replace NiCd batteries with NiMH ones - they are both about 1.2V/cell and have similar discharge curves. If the circuit has a low-voltage cutoff designed for NiCd cells, you will probably not be able to get all the power out of the batteries because it will switch off too soon. NiCd also has better high-current capability (although I doubt that the Game Gear takes enough current for this to be an issue) and about twice the self-discharge rate. Against this, modern NiMH cells have much higher capacities than the old NiCd batteries in the same form factor so even with a premature discharge cutoff you will likely still end up with more usable battery life. Li+ batteries have much higher capacity than anything with a Ni based chemistry, but they are completely incompatible in electrical terms - most basically because they have a terminal voltage that's about 3 times that of NiCd or NiMH cells and also require a different (and much more complex) charging system. It would probably be possible to design a battery pack for the Game Gear that used a pair of Li+ cells, but it would require a ground-up redesign of the charging system.