Hi allstar, the probable answer is yes you can use the old case.
Presumably the case is ATX format, which means that when you shutdown your computer, it turns itself off after Windows has closed.
Some computers, especially from the likes of Packard Bell, HP and the like often have their own peculiar designs, and are not really suitable for upgrading. Some also use micro-ATX, with onboard graphics and sound, and only about 3 pci slots. These may not have enough space for a full ATX motherboard. A computer of the age of yours probably only has a 250W power supply which probably isn't powerful enough for your new computer. Open the case, and you should find the power rating on the supply.
If you want an upgradable system, you may need a full size ATX motherboard which is 12in x 9.6in (305mm x 245mm). The power supply shouldn't be too much of a problem. You can get quite a good 400W supply from EBuyer for under £15 click here
What is an equally important question is whether the case will take all the bits you want to fit in your upgrade.