in this old measurement tools check power supply caps, mostly higher voltage (400-450V) are the problem.
this problem can be keramic caps for digital chips (cpu boards or so)
have you picture from inside?
installing retrofit document can little help.
08566-90151-retrofit.pdf (4410.18 kB - downloaded 101 times.)
service and repair manual to big to post, find in keysight page
Part Number: 08566-90042 (Dec84). This manual is provided for information only. The 8566B and 8568B are no longer sold by Keysight. Note: the file size is 36.37 MB.