The batteries will physically fit the newer tools since DeWalt kept the 18V connector the same across their lineup, but there's a catch - those old NiCd batteries won't work with modern chargers. DeWalt switched to lithium-ion tech years ago, and their newer chargers are designed specifically for Li-Ion batteries. Trying to charge old NiCd cells in a new charger will either not work at all or could damage something.
That said, if you still have the original charger from 2008, those old batteries should still work in it and then slot into your newer drill just fine. The tool itself doesn't care what chemistry the battery is, it'll run off NiCd or Li-Ion without complaint. The real problem is that NiCd batteries lose charge way faster when sitting around, and they don't last nearly as long per charge compared to what you'd get from a modern lithium battery.
If you're looking to save money, honestly your best bet is just picking up a basic Li-Ion 18V battery and charger kit. They're cheap these days and way more convenient than dealing with old NiCd cells that drain quickly and need the old charger dug out every time.