I have dedicated lines, but why is this happening?

I had this exact problem. For me, it was a bad tube in the right side of my phono stage, plus a different tonearm cable. It was all phono related for me. Not sure if that applies in your case.

Ah,you may have a grounding problem.Recheck the outlet ground and more importantly the ground connection at source.
If you have a basement you can drill a hole in the floor and drive a new ground rod.Run a separate ground wire from your outlet to this new ground rod.If you have an outlet like from PS Audio which has an isolated ground this is perfect because your outlet box and stuff is grounded normally and the isolated ground is all that is connected to our new ground rod.They may be i dunno $100 or something but the best improvment period in reducing noise and of course less noise means more music.Hope this helps.
Peter

ground your dedicated line to the box (fuse panel) instead of the buse bar. kurt

Why bother with dedicated lines if you don't isolate the grounds? As to the air conditioning popping: don't have a clue, but maybe it's related. peace, warren

It may be time to look at the A/C unit as the source of the popping. Areas I would look at include making sure all the electrical connections are tight and corrosion free. Obviously do this with A/C breaker off. Don't overlook the exterior disconnect box as those contacts may be showing signs of corrosion/oxiditation. Also you may want to see if the A/C is low on refrigerant as this can cause increased load during start up.

As far as Peterd's suggestions, I've never been a fan of floating grounds (ie a ground bar that is not tied to system ground) and they are specifically prohibited by the US National Electric Code due to shock hazard potential. For what it's worth ground rods work better in moist soil and the recommendation is to locate them outside at least 1 foot beyond the spill line of the roof so as to take advantage of natural rainfall.