The Sega Dreamcast Controller ports can sometimes stop responding, I’ve read that it can be as a result of disconnecting and reconnecting controllers whilst the console is switched on. The cause is a blown fuse, marked F1 on the controller port circuit board.
I recently purchased a faulty Dreamcast with this problem just so that I could try this out. When I was searching for a fix, I found this page by Luke Benstead/Kazade. It contains everything you need to know and is an excellent guide.
I’m not going to go into lots of detail, I recommend you check out the original guide. Below are my pictures and some brief notes I made when fitting a 72V 400mA PolySwitch Resettable Fuse.
I found it much easier to remove the old fuse by adding some additional solder onto where it is soldered onto the circuit board.
After sticking the legs of the new PolySwitch Fuse through the holes, bend them in opposite directions to hold them in place.
Solder the legs in place and trim them nice and short.
Job done! You might notice the black battery holder I’ve also installed.
Again, here is the original guide I recommend following.