How to repair seagate momentus 5400.6 if the usb port is broken

How long have you had the drive? If there is any warrenty left on the drive you can sent it in to seagate for repair. If the drive is inside an external enclosure then you can take the drive out of the enclosure and connect it by sata internaly or esata externaly if you have that feature on your motherboard.

On my external drive I was able to take it apart and re-solder the usb connector. Chances are that is what happened to yours - broken solder connection. If you don't have those skills maybe somebody you know does.
-Bruce

Yes thats whats happen would an Vantec Hard Drive Enclosure work?

I bought it in the beggining of August,2010.

Not 2010, 2011

One option would be to solder it. If you need to use the external drive to take save information between computers disregard this. If you only use the external drive for more space on one computer you can remove the case and install the hard drive in your computer.