Quick question - where are the ports/card reader that are broken? Are they on the front by the floppy drive/CD drive? Or are they on the back by where you plug the keyboard, mouse, monitor in, etc?
If it's the card reader/USB connections on the front that are broken, then it should be cheap and easy to replace them with a new unit - they normally fit into a 3.5 inch drive bay (just like a floppy drive would) and connect to the motherboard via a cable.
If it's the USB connections on the back that are broken, then there's also a chance that there are some pins on the motherboard (the big circuit board inside the computer) for connecting external USB devices (such as the card reader that I've described above that would fit into a 3.5 inch drive bay), so you could buy one of those to use instead of the ones on the back.
Alternatively, if there are no pins for connecting an external USB device on the motherboard, then it may be possible to buy a PCI card with USB connections on - this would fit on a PCI slot on the motherboard, assuming that you have a free one on your computer. The PCI slots are normally used for adding things like sound cards, TV cards, etc.
Am I right in thinking that the connections for your keyboard, monitor and mouse all work OK?