A squealing that gets quieter when you touch the strings but is still there with other basses is a head scratcher. When you say squealing is it high pitched and the pitch changes? Does it sound like feedback from a microphone and very loud or are we talking about something more subtle that's a 60 cycle harmonic?
The most common issue I come across in amps is the switching jack/s for the effect loop/s that get oxidized.
looking at this thread on talkbass it sounds like there might be an issue with the mute circuit for the DI and perhaps something fuzzy with the built in octaver.
https://www.talkbass.com/threads/proble ... ad.484967/ One of the posters on TB is the designer of that head's preamp and you could contact him or her directly if you join.
I'd start with a search over at the music-electronics-forum.com If anyone knows about it or has dealt with it before they will have posted over there. I did find this thread:
http://music-electronics-forum.com/t14470/