AC condition

A power conditioner. I won't get into brand specifics, you can research that. What's happening is that devices like compressors which are found in refrigerators, AC compressors, etc. draw a large amount of current at startup, much larger than when they're on at "steady state". These current spikes cause noise on the power lines throughout the house and voltage drops because of the large current draw. This is what you're seeing. Given that the AC compressor is probably 240V 3-phase, changing to another outlet won't help as the effect is being felt in the entire power grid of the house. A power conditioner and/or regenerator such as PS Audio Power Plant, into which you would plug you TV and audio equipment should take care of these effects.

It sounds like the compressor in your A/C unit may be having a problem starting. This can happen more often as the voltage supply drops. It causes the compressor to load down your electrical for a longer time. Call an A/C company and have them install an item called a hard start kit. I helps your compressor start faster and cause less of a load on your electrical service at startup. They are also easy to install if you are mech. inclined. This may not fix your issue entirely but may shorten the effect. I put this item on any units I work on.
Also when was the last time you had the electrical connections tightened on your service?