Which of the GX620's do you have?
Apparently, there were different versions for 4 different cases.
According to the information I could locate, if you have the Mini Tower version, it does have a full height PCIe slot.
If you have one of the others, you will be limited to either a half height PCIe card or NO PCIe connector at all.
Even if you do have the Mini Tower version, I doubt a 9800GT will work with it.
My understanding is everything is very cramped in that case.
While it may fit height wise, it probably will not fit lengthwise.
Adding to that an old and dubious PSU (which will not have any PCIe power connectors BTW), I would recommend against it.
I recommend using a 4670 instead of a 9800GT.
Not only is the card much more compact, it is designed to draw very little power and work in the types of system you have.
You can locate 4670s in the wild for around $50.
Just depends on what version you have as outlaw said. Anyway if you go with the newer 9800GT that doesn't require a PCI-E connector, your PSU should be good enough. It would be a good idea to take out some measuring tape and see how much space you have between the plate where your PCI-E slot is and the drive cage likely to be placed in front of it.