sounding more like an electrical problem.
How old is the battery ? These puppies are very sensitive to having the proper voltage.
Could also be a ground / cable problem with the battery.

I don't like the 'radio cuts off' stuff ......
Does the car continue to run OK ? [ nevermind - you said it 'lags' ]

Might want to pick one of those voltage meters that plugs in the cigarette lighter socket from AutoZone or Advance and see if the voltage is dropping while these shenangins are happening.

or here's a good one from Amazon.com :