Well, in highschool I used to do a lot of painting/restoring on old sportcars.
Much of the interiors were vinyls and plastics much like most guitar cases. One thing that might work is take a mildly abrasive pot scrubber spounge, get it wet and lightly scuff away the paint. Depending in the type of paint they used it might work, might not.
However, if it doesnt work, or scrubbing it scuffs it all to hell, maybe go the the other route. Get some special vinyl paint or vinyl/leather dye and repaint/dye the whole thing. Special made paints like that work pretty good on vinyl car seats and interiors, prolly vinyl covered guitar cases as well. They are flexible and wont peal off. You can probably buy it at some auto part shops or specialty paint stores.
If you paint it, take your time to do a nice neat job. Be carefull of overspray and drips. Finish it off with some satin clearcoat and it should look good as new and be pretty durable. I have done many trophy winning interiors that same way back in the day. It works great for covering up bad stains or discolorations.
If you use vinyl/leather dye, its a little easier to apply because it works like shoe pollish. But using that you would most definatly want to get all that paint off first, because it doesnt cover like paint will. It will likely take several coats and buff it with clear shoe wax. This method might look a little better but will be a lot more work. You definitly would need to get all the crap off the case to a good clean even surface.