My 04 Monte shakes and vibrates extremely bad on the passenger site and in the steering wheel only when I'm on the gas or go in up the slightest of an incline... As soon as I let off it stops...please help it's driving me crazy... What could this be?? My check engine light also stays on all the time now...

 

The vibration could be a bad tire, bad axle (more than likely the cause) or something broken in the suspension, or a bad transmission mount. If it goes away when you let off the gas it is probably the axle needing replacement, well technically it is the inner parts of the axle but for the time it would take to pull the axle out and rip it apart and re seal it, it is honestly easier just to replace the axle. But before you do make sure you give the ball joints, and control arms and everything a once over to ensure they are in good shape, also check the brake rotor to ensure it is not warped, and finally make sure you swap your tires around as if the tire itself has blown a belt it could cause the shaking or if it has become unbalanced. If the vibration moves when you swap tires you know it is either the tire or balance, and could even be a bent rim. Any and all of these will cause vibration in the front end.
There are probably more possible culprits that I am missing but these are where I would start first.
After reading your post againg I am about 98% certain it is the axle.

For the check engine light, go to parts store and see if they will read your CEL code for free, once they give you the read out you can post back here with what it is and we can tell you what the code means and what needs to be fixed, or click on this link and look it up

http://www.troublecodes.net/gm/


Hope this helps you a little bit