When I drive at speeds over 30MPH, there is a vibration through the entire vehicle whenever the accelerator is being pressed, but it disappears as soon as my foot is off the gas. The severity varies from a light shaking to a heavy vibration and is not a consistent problem. Any thoughts as to what could be causing it?

 

What year/mileage?

For starters, scan for codes & clean the MAF. Jack up the front end and look for loose parts. Bad CV axles can vibrate when accelerating.

 

Fuel injector, Coil, or Spark Plug would be my first guess. Although I believe misfires would instantly cause a check engine light.

 

It's a 2003 with 162000 miles. The inner boot on the RH CV axle is half gone. It doesn't appear that the knuckle is loose, but I can't really get good leverage to check it while it is just jacked up. But this is probably the problem.

 

The CV axles can cause vibration under acceleration that goes away when cruising or coasting. Even with the boots and everything intact.

When you say "press the gas" are you talking about getting on it or lightly pressing the gas to keep a speed?

If it feels more like a vibration than a misfire it's most likely the CVs.