Maybe you might!
It's some work, but there are fuse links on the USB power feed lines so you might be able to save the logic board.
I should point out these are SMT components so you do need to have good soldering skills and will need to use a meter to measure the voltages.
I would first check out to see if the USB ports are still working (just not able to power the device). Using a new powered USB hub and a known good USB device connected to it (i.e. HD or thumb drive) can you get the port to see the drive. If you can you have a chance here, if not, sorry you burn't the controller on the logic board.
Also check your power lines using a cheater cord do they offer power? As you could have burn't something else.