One of my tube amps has a slight buzz when overdrive is clicked on, it goes away when I start playing. I'll guess that's not what you're talking about.

Amps do die. If you have less than several hundred $$s in it, it's probably not worth checking out (as you said) and will need to be replaced. Unless it's a worn plug-in (like for the guitar cable) or a bad connection in a circuit, most are really not that repairable anyway other than by the swiftest of hobbyists or amp techs.