this is for esmith69

I doubt a capacitor would help your situation unless you have a whole bunch of accessories like amps, neon lights, etc.  Does the problem happen when you have the CD on or the radio on?  Or does it not matter which source is being used?

There may be an illumination wire in addition to a dimmer wire, on the head unit's wiring harness.  Basically any wires on the aftermarket head unit harness that have any orange in them should not be connected to the vehicle's wiring.

There's a couple ways to go about troubleshooting this.

First I would suggest disconnecting and temporarily taping off all of the head unit's aftermarket harness wires, except for the +12 volt constant, +12 volt switched, and ground connections.  These should be yellow, red, and black respectively if the head unit was made within the last 5 or 6 years.  These are really the only 3 wires that are necessary for the head unit to turn on and function properly (though with no speakers connected you'll obviously not hear any sound).  Then try to turn on the dimmer and see if you still get the problem.  If it goes away, then there's something wrong with one of those wires you just temporarily taped up.

If the problem still occurs, you're probably gonna want to use a multimeter to test the +12 volt constant wire at the radio's harness, for voltage without the dimmer/interior light on, and then while still looking at the multimeter display, switch the dimmer on and see what (if anything) happens to the voltage.  If it drops significantly then you'll probably need to run a new +12 volt constant wire.  Also do the same thing for the +12 volt switched wire, and if a severe voltage drop occurs here too then you'll have to go to the ignition harness to get your switched power.

If you don't have a multimeter or don't feel comfortable using one then the only other thing I could suggest would be to run a new 15 amp fused wire directly to the positive battery post.  Then the other end goes to the head unit's yellow (constant) wire.  But if the problem lies in your switched 12 volt hookup then that probably wouldn't solve the problem, but I don't think it's related to the switched wire.

What kind of vehicle do you have (year/make/model)?  And what is the model number for the head unit?