Do you have experience (and tools/test equipment) fixing amplifiers?
Schematic is available here:  http://elektrotanya.com/hughes_and_kettner_matrix_100_amplifier.pdf/download.html

 With inexpensive practice amps, it is not uncommon for the circuit boards to be secured only by the pots.  Often what happens is the amp falls on it's face while there is a cord plugged into the input jack.
This often causes the board to bend and breaks the pots.
Inspect the input jack to be sure none of the solder joints have cracked.
The best way to check if some pots are good is with DMM measuring ohms.
Also you can look with a magnifier to see if the carbon track is cracked (in the same area where the bad pots are cracked).

  Most of the picoscopes can only handle small voltages (20V or less?) so if you are wanting to work on tube amps you will probably need 100:1 probes.
  Recommend doing further research on their limitations before you purchase one.

+/-15.7V does not sound right for the supply rails, unless you are talking about the low voltage supply.  The power amp should be running on higher voltages than that.
Without a schematic there is not much anyone can suggest.
  The schematic does not seem to be available online unless you buy it here:
http://www.majelectronic.co.uk/

1)  A switching jack (cliff) was wired in SERIES between the Fender combo amp and it's speakers.  It was wired up to be an input to the speakers, NOT an output from the Fender amp.
  This enabled the Fender combo's speakers to be used as if they were a separate speaker cab.
2)  The Fender speakers were re-wired so they would be in SERIES (16 ohm).  The stock wiring had been parallel (4 ohm).
This was because the Vox amp had an extension speaker jack that was rated for 16 ohms, and the Fender speakers were to be used as an ext.spkr. for the Vox amp.

  Not sure what you could do to increase the reliability, sorry.
But I will mention that before you connect the new chips, the power supplies in the amp must be fully discharged.
  Otherwise you can blow the brand new chips before you ever turn the amp on.

  This may not be your problem but I will mention it anyway.  When you convert a combo to be a head, you often have to add a speaker jack, did you?  It is important that this jack be completely insulated from the chassis, otherwise you can get a ground loop/hum.  If you use a plastic jack, it should be insulated, but if you use a metal jack, you will probably have to use insulating washers so the jack ground does not contact the chassis.
  In your case, it sounds like the hum is only from the OD channel.  But it is possible it is there in both channels and just less noticeable on clean due to the lower gain.

Here is the complete schematic

 Have you tried Enzo's fix from reply#6? 
Is this a problem that was definitely not there before?  Or a problem that may have always been there?

  We still come back to the problem that some pickups do it and some don't.  And the problem only occurs at highest gain settings.
  When it squeals with the guitar connected you said it stops if you turn down the guitar volume a bit.  How about if you turn down the master?  Does it stop squealing with high gain settings when you turn the master down?
  The idea that it is not the pickups because it does it with a cord plugged in but no guitar connected is not logical.  Any high gain amp will squeal under such conditions, it is to be expected and perfectly normal.
  I am not saying there is nothing wrong with your amp, only that so far there is no proof this is not normal feedback.  If it is really a problem with the amp, I can't understand why it would be pickup selective.

  No offense intended, but if you are unable to identify transistor types, how did you come to the conclusion that the original one was bad?  Was it blown up or burnt?

  Thanks midibob!
For anyone needing to repair one of these, midibob's daughterboard is priced very reasonably.
  He doesn't want to list the price here in case it goes against forum advertising policy, but send him a PM if you need one.

Quote from: gdeig on August 23, 2013, 06:36:21 AM
this doesn't explain why the exact same  oscillation tone can be heard with no guitar

Quote from: gdeig on August 21, 2013, 11:11:23 PM
Ok, if i short out the input or there is nothing plugged in (same thing) there is no squeal.

These 2 statements can't both be true, which is it?

  That's quite something midibob, thanks for sharing!
How much do the daughterboards go for?

As a tech for over 35 years myself , I have grounded these amps , a real tech ALWAYS , finds a way to ground ANY piece of equipment they work or they will wind up DEAD
[/quote]

Well, if you are grounding these kind of amps (widow makers) without using an isolation transformer that is just not safe.  Roly has explained why.
  You said that an isolation transformer is "not absolutely needed".  That is wrong and unsafe.
  Maybe you could explain why you would want to short cut around the safety that an isolation transformer provides?  I'm sure you are aware that such an amp would be illegal to build and sell today due to safety reasons.