Hi. I've bought an Advantest U4941 that its hardware is very similar to your Advantest.
Here is a good thread about the Advantest U4941 that however, its cards are a bit different to mine Advantest, but it don't mind.
https://www.eevblog.com/forum/repair/advantest-u4941-portable-spectrum-analyser-repair-by-fraser/Well, mine Advantest had similar fail than yours. I found that tiny SMD capacitors were dry, with big ESR, especially 6,8uf 25V. Fortunately it's caps did not spilled electrolyte to the pcb.
The other capacitors had a bit of ESR, but not fatal, more the big capacitor is more good the ESR is.
However, I replaced ALL surface electrolite capacitors and, it worked.
I passed the calibrattion and it worked.
I found another fail, the signal amplitude changed between high and low RBW, but it solved itself changing RBW, I suspect a relay located in the RF module.
I replaced 6,8uf 25v caps by 10uf 50v value. I replaced surface capacitors by normal radial capacitors, placed carefully.
I hope this information can be useless and your Analyzer get repaired. Best regards