Is it really worth the effort? More often than not, I saw that era board fail from burst capacitors.
Till some point in the XP era, many boards ran the CPU VRM from 5V PSU rail and the current swings at CPU state change were so high that to maintain maximum stability, many bios disabled one of the power management modes so the CPU essentially never went into a halt idle state, wearing the capacitors faster (in addition to generic capacitor plague) and wasting power.
This wasted power also meant they needed more (average) airflow even for routine tasks, compared to the next generations of CPUs, and this also increased maintenance through higher dust accumulation.
I have cleaned a few boards, mostly dry cleaning of spider webs (which is what I suspect your "tin whiskers" really are) and dust, and wet cleaning if it was a smoker's system.
Wet cleaning I just take the battery out, spray about 10% solution of Mr. Clean on it, let that soak for a minute, immerse in warm water and go over the board with a soft ~ 1.5" wide paint brush, same paint brush I would have used to dislodge dry dust if it was a bit stuck on.
Next I rinse the board with tapwater and put it in a tub with water and a drop of either dish detergent or dish washer rinse agent. This drastically decreases the surface tension of the water so you don't get droplets clinging to things.
Next I remove from tub, shake off excess water or compressed air if available, stand the board up on end and if in a hurry will point a fan at it, otherwise wait a couple days for it to dry.
I
usually do this to redeploy a working board or one that had some card contact issue, not trying to magically repair a board that has a severe enough fault that it won't even stay turned on.
When I wrote usually, it hasn't been that often, usually by the time a board is that bad it is obsolete but every now and then I have been brought systems from people, like a family friend or friend of a friend, with special circumstances, severely limited income and difficult to teach changes to, so I try to just keep their system running with least cost and time invested by anyone.
In retrospect, it probably would have been better to just look inside the system and tell the owner to get a refurbished OEM replacement, but my crystal ball was broken as far as how much advancement to expect in the PC industry over the years. Today, something that runs IDE drives or maybe SATA1? It's the combination of that and probably due for a new PSU too, to salvage something that has reached a reasonable end of life.