I'd try a couple of things to debug this.
First, have you changed anything else in your rig since the problems started? Amp? Amp settings? Effects? Cable (probably not if you're using the 5-pin cable!)?
Second, I would try another cable (at least in the 1/4) just to see if that's part of the problem.
Third, try another amp (even a guitar player's amp) and see if the problem doesn't go away. If it does, the problem is your amp or it's settings (too much high boost).
Fourth, clean the internal and external connectors. I'd see if you can find a Caig Labs DeOxit or ProGold cleaning pen. They're ridiculously expensive (over $20). It's a little metal pen-like container with a tiny amount of cleaning solution in it. The cleaning solution is good, but the really good part is that the pen has a special fiber tip that really does a good job cleaning connections. When you use it it applies the cleaning solution and lets you scrub the connector really clean. You'd want to use this on the molex pins on the EQ boards, the jack and plug and any other electrical contacts.
After this stuff, it will be more difficult and expensive to work on as you'll need to start swapping stuff around.
When you get this squeally noise, it's a combination of a lot of treble boost and some noise that's getting into the pickup circuit. Sometimes noise or a failed component can start injecting noise into the circuit at a frequency higher than the bass is producing. But the preamps in the bass will happily amplify it which can push them into overdrive or feedback.
Your description of things sounding thinner strikes me as a change that could be elsewhere in your chain, so I'd try to eliminate that possibility first. If you plug a different bass into your rig and it sound thin, then the problem is with the amp; if not, then the problem is in the bass.
Good luck,
David Fung