Little update on the HP 53310a.
Since electrolytic was poring out of the PSU I recapped the whole thing.
So decided to do a quick test just after, half expecting a success. But nothing happen. The PSU was just dead.
Quickly started debugging the primary and found 2 open resistors. So apparently the electrolytic all over the board shorted the 2 pins of C3 and R13 and R14 just died with all the current flowing through them. The funny thing was that the main and secondary fuses were fine.
Replaced the 2 resistors, double checked everything on the primary side, and everything looked in order this time.
Tried another power on. So the good news is the psu is alive now but the bad news is that he is suffering from a bad hick-up. Probably got something on the secondary side loading one of the power rails.