Help! Power question

It sounds like the power going to the audio rig is not on a separate circuit.  Contact an electrician to confirm your house power configuration and service amperage. If the house service amperage is insufficient, then maybe your rig is suffering a transient brown out condition. I’m not sure a surge protector would help in that case.

Mlapenta, you are experiencing a massive dip in your current from the panel....line conditioners only massage the voltage.  When the ac kicks it has a high instantaneous current draw to get it going...the ac is 240volt so it is fed by both phases of your panel, therefore you can not escape it entirely, but you may be able to mitigate the effect to where it no longer causes your gear to freeze.  Many things could potentially lead to the prob, but the most likely is you have At least 1 of several things (or a combimation of several things) occurring that would cause an end effect such as yours:
- You have a 100 amp panel and the a/c initial draw is a very hi percentage of that, causing a dip housewide that effects your equipment
- your panel was out of empty breaker locations, so the ac installer used the spot for your audio line, and then just threw them on the same breaker....check inside your panel for 2 wires going into one  of the ac breakers (ac breaker will be a 2 pole which occupies 2 slots in the panel....the ac should have 2 wires going in....1 per screw clamp....if there is 3 wires going in, with 2 under any one screw clamp, then that is what they did....)  also be sure to check the breaker for the air handler which could have the same scenario going on.
- your panel is so old that the dielectric is effected, thus minimizing it's amperage carrying capacity. Is there rust in there? 
- loose connections on your equipment or thru the line will increase the impact of the drain...
    - are your cords secure in the outlet and at the rear of your equipment? ...
    - is the outlet secured firmly to the wall?
    - Is the outlet damaged? 
    - Are the splices (if there are any) within the outlet box solidly connected by being  twisted together under the wire nut, or are they just put next together with a wire nut twisted on top of them
-  is the audio equipment home run at the panel secured properly to the breaker, the neutral bar and the ground bar?

Make sure your power is OFF before you start messing with teceptacles, the panel, or any exposed wiring! 

Hope this helps & best wishes!

PS. ... IF you are not familiar with electric wiring and experienced at handling it, an electrician is really the way you should go, with 1 word of caution.... if you are not familiar with the electricians reputation, ensure he checks everything, rather than just walk up to the panel and say you need a new one. ..   big job... big $... he likely wouldn't lie, but that doesn't mean it is the simplest solution to the problem you want fixed at this moment when securing connections might do the trick for $100 instead of a thousand.