I had a PS from an E4406A that had the same issue (dead standby power). I traced it down to the little PWM board just before the transformer by removing the transformer and injecting 15VDC into that side at an appropriate spot. Used it that way for a little while, then acquired another E4406A in better shape. Used that one for years and finally circled back to this.
Two caps: 47uf and 33uf. Both came in at 22uf, and ESR of around 20ohms @ 120Hz. I had an exact match for the 47uf, but had to use 22uf+10uf in parallel on the backside of the board to get it going (frontside has interference with the main caps).
Works great now....
Edit: Now that I think about it, though, that circuit is probably pushing far beyond 120Hz.... I haven't really looked at the datasheet for the SG3843D.