Motherboards in that era mostly used tantalum or ceramic capacitors. If they're not shorted out, I'd leave them well enough alone. Tantalum capacitors of any era can explode or go on fire unpredictably, unless they were insulted with a voltage spike, then they're pretty much guaranteed to explode or go on fire. Tantalums are very unforgiving to overvoltage events. The only thing that should be checked is if there are any actually shorted tantalums by measuring the power rails, if there are none, they're fine to use.
Ceramic capacitors likewise are also very stable, generally the only thing that can take them out is mechanical stress that cracks the plates, which most of the time will result in a short, but sometimes an open circuit.
The power supply is another story, those can have all sorts of strange faults, especially if the capacitors have leaked onto the board and other components. The electrolyte can wick inside components and cause them to fail in any number of ways. I don't recommend powering up an ancient power supply without first checking it out, and definitely not attached to anything important. Old SMPS units generally do need some type of minimum load though, or they will behave erratically. In some cases, they can destroy themselves.
If you intend to dabble in the dark arts of ancient computers, learning how to solder is a basic requirement, unless you have a bottomless pit of cash to burn. Tantalum capacitors can go off at random, and it's going to be hideously expensive to have to ship your motherboard thousands of miles just to have a single cap replaced every time it happens. Through hole soldering really isn't that difficult, if you want to make it easy, buy a desoldering gun/station so you don't have to faff with solder wick or those nasty spring loaded solder suckers.
