Very load thud feels like running somthing over every foot,when going backwards in reverse or neutral.when appling brake or not.just got it out of the shop new fron pads and roters.

can you push car backwards, in neutral ? (sure on a flat driveway)
yes, then the trans is failing. not brakes, easy test no?
or jack wheels up , an feel them can you spin them easy.?
can be bad transmission shifter cable , not allowing the trans side
to get in to Reverse at all.
we check this too.
check transmission levels (fluid) yet, using book way, not guessing.
do not check trans like any engine. ever.
do not over fill it. ever. read the operators guide first. then act.

If you put it in neutral with the engine not running and have someone push it what happens?

These are common for stripping the splines in the torque converter for the pump shaft. If it did this when you check the fluid with the engine running it will read overfull. To fix it you would have to remove the transmission and replace the torque converter.

Is it only when you go from park to reverse? Or is it just as bad going from neutral to reverse? I've noticed on mine that it's often tight if I park on even a slight slope. If it only happens when going from park to reverse, try this. Hold your foot on the brake, and put the car in drive. Keeping constant pressure on the brake, go back to park, then back into drive. Did you feel the stiffness when you had your foot on the brake?

just keep your foot on the brake. It cannot do any damage, the auto box is designed for this

If you put in neutral you risk making a mistake and selecting reverse. or may not select gear inadvertantly on a hill and roll backwards.

broken gear in the trans. i hate to tell you but the trans needs to be rebuilt or replaced.

The lights have nothing to do with your car not going in reverse. I know this is going to sound silly but, are you releasing the parking brake? That brake is the lever between the front seats. Are you taking your foot off the brake?

I know they sound silly but you would be surprised at how often this happens with th eparking brake.

When you put the car in reverse can you feel the transmission engaging? You should feel a slight **** when you put it in reverse with your foot on the brake. If you are not feeling this, your transmission needs to be repaired.

The transmission moves? In what way? If under hard acceleration your motor mounts could need looking at. Put vehcle in gear parking brake on foot on brake pedal and give it some gas then sudenly let up on gas. If you feel a thud, the tigh motor mount is probably your culprit. You can test the left mount same way but be extra carefull, your psrking brake won't hold as well so use the foot brake when accelerating . Acceleration need not be alot, just enough to make it do what you feel or hear. Motor mounts are not a major problem. good luck

Check you transmission fluid level and if it's not your transmission, I'm thinking that your brake shoe lineing in the rear brakes may have separated and is jamming up aginst the drums when your trying to back up. Sorry can't halp you with any more, good luck and start with that and hope it help's.

As far as I know the procedure should go something like this...

Stop the vehicle, engage the parking brake and if applicable, get out and turn the hubs on the front wheels from Free, to Lock.(You may not have these on a Suzuki, they may be auto-lockers)

Get back in the vehicle and put the transmission shift selector into Neutral.

If you have a manual transfer case, move the selector-shaft to 4x4-High, or 4x4-Low -- whichever is desired. Now, putting the vehicle in gear with the transfer case is sometimes somewhat difficult. As long as the vehicle's transmission is in neutral, don't worry, the gears inside the transfer case are big and beefy -- Don't be afraid to be rough -- Again as long as the transmission is in neutral. You may also have to disengage the parking brake and slightly let the vehicle roll forward or back with your foot-brake to get the Transfer case to lock into place.

Once 4x4 of the selected High, Or Low range is selected, usually indicated by the vehicle jerking slightly with a slightly loud clank/thud. Move the Transmission selector out of neutral into your desired gear (Drive if Automatic, if Manual, whichever gear you pull out from). and voila! You should now be in 4-Wheel-Drive.

To disengage 4-Wheel-Drive. Just reverse the steps.