Thanks for the tips!
The battery in A4000T is a coin- battery, only model that didn't come with the acid-barrell- type, as far as I know anyway. So it's not supposed to be charged. However, I will replace it as its a cheap test to see if things improve.
Still, as this problem has been creeping up, slow but steady, I get the feeling that it is some component/s that has been wearing out over the years. Don't know exactly when my unit was manufactured - it has no factory markings whatsoever - but the age must be closing in on 15 years.
Not sure about the PSU how it could be damaged in such a way so that it would give these kind of symptoms. Ive had this machine jammed with hardware like CSPPC, Mediator, Voodoo, P-IV etc. How can I know if the PSU has been damaged?