My controller cuts out sometimes, (only port one).
Occasionally, my controller will cut out on me. It used to simply cut in and then out, as if it had been unplugged and replugged quickly, sticking my analogues and shoulders in currently held positions. Now (still rarely) my controller will simply 'lock' and not allow me to do anything, unplugging and replugging has solved this thus far. It's probably an issue with the metal conductors in the individual port (or not, I don't know). Either way, I need some more permanent help.
You're probably right in that its a bigger problem, but it could also be as simple as a cable connecting the port being a little loose. You can try opening it up to see if there is anything obviously out of the ordinary or corroded.Gamecube Front Panel
NOTE: You're going to need a special 4.5mm "Gamebit" driver to open up the case.
UPDATE: You can try the DIY pen trick for an easy driver DIY Gamebit Driver
Or purchase a gamebit here: Gamebit 4.5mm