Firstly, as Rey305 mentioned, there's definitely a problem on that pad sensor's connector, which would cause the pad problems mentioned. I think that's going to need a pad sensor replacement. (It looks like it would be difficult to just fix those broken tracks.)
Two issues that can cause extra inverter noise (high pitched square-wave type sound that seems to be coming from the inverter or the power supply)
1. Bad capacitor C1 inside the inverter:
Symptoms: noise seems to be coming from the power supply, noise also present in the audio outputs.
If you are going to recap the power supply, it's well worth replacing one of the caps in the inverter too. Because the one electrolytic cap in there is responsible for filtering out the high frequency noise from the inverter - if this cap isn't working properly, the inverter noise leaks back into the power supply and makes a lot of noise there - and the noise also makes it through to the audio outputs.
The main guts of the MPC60/60II inverter are covered by a metal cube-shaped, erm.... cover. Have a look underneath the board, you can remove this cover by desoldering the 3 very large solder points. Now lift off the cover.
You'll see one electrolytic capacitor, C1. It's 220 microfarads, 16V. This is worth replacing.
2. Loose metal cover around the transformer T1:
Symptoms: Noise coming from the inverter, audio signal is not affected.
Notice that the small transformer on this inverter circuit is surrounded by a circular metal 'ring', and it is only very loosely held in place by a little piece of dried-out old tape. Take off this metal ring, gently slide it off. Now wrap some electrical tape around the ring so that the metal of the ring won't touch that metal cover when you replace it. Slide the ring back into place over the transformer, and take another small piece of electrical tape and stick the ring to the top of the transformer - this stops the ring from moving about or slipping off, something else that increases noise in the inverter.
Changing capacitor C1 should eliminate inverter noise from leaking into the audio. But the inverter itself might still make some noise, it doesn't seem possible to silence it completely. It also depends a lot on the backlight, some just cause more noise than others - I'm working on that

I should take some photos of the inside of the inverter so you can see what I'm talking about..... coming soon...
Matt