Shutter curtain only opens on slow speeds up to 1/30s.

This camera uses a curtain focal-plane shutter. The bearings often need some lubricant as well as the gear train.

The trick is getting to them to clean things and then lube.

I can't say definitively that your camera doesn't have other problems, but I used to do this kind of work. You have a timing problem. If you got no exposure only at higher speeds than reported, I'd say your second curtain is overtaking the first curtain, a rather common calibration problem. This is generally a pretty accessible adjustment, although you would still need test equipment to do it. But for the SLRs I've seen, 1/30 is the slowest speed at which the first curtain opens all the way before the second curtain starts. I don't see how the second curtain could then overtake at 1/60. This means you have a problem with the shutter escapement, which is a bigger deal.

Camera disassembly is a pretty delicate operation. I don't know this model, so I don't know how much disassembly is required to fix it. You need to measure curtain speeds, which requires expensive equipment you don't have, in order to determine the exact problem.