You won't be able to enter DFU mode without a working USB port. It relies on the data connection to enter DFU.
I'm pretty sure a repair will be a sizable charge, but you should probably take it to an Apple store to find out.
BEFORE you do, make sure you do the following. Whilst you don't have a warrantly, there is no harm in disgusing the jailbreak.
1. With the device charged, remove all the apps / themes / tweaks etc. which you have installed via Cydia. Make sure it looks like a normal unjailbroken device.
2. Stick the Cydia icon away in a folder somewhere that won't be seen unless someone trawls though all your folders (A genius won't do that).
3. Hold home and power for 30 seconds. This should place the device into recovery mode (even without a working port). You should see the "connect to iTunes" graphic on screen. Don't let go of the buttons until you see this graphic.
Return the device to the store in this state. A genius will connect it to their PC and see it is not working properly. They will then quote you for a repair, and you can choose what to do.
Oh, and IMHO, your jailbreak has nothing to do with this at all. It's just bad luck that the age and wear has eventually caused the 30 pin connector to fail. It happens on old devices. Nothing to do with the software you have installed, including the JB.
Hope that helps. Good luck.