Water entered inside the gerabox after aflood

Have someone watch the engine while you step on the gas( e brake on and tires blocked so that the car cannot move) to see how much movement the engine does. You may have bad engine/transmission mounts.

Check your coolant level, your water pump and thermostat

Describe the noise. It sounds like you have a blown head gasket though

if you have an automatic gear box , then it is very possible that you have reverse band is broken inside gear box , , light will come on because switch for reverse lights may be actuated by shift lever not gears .

there is a foward band and reverse band in auto gerabox's so if you are able to drive forward this gearbox will need to be repaired or replaced .

if manual gearbox , you may find a reverse linkage loose , or gears dammaged in gear box .
good luck hope this helps

this sounds like a fault with the solenoids in the box, especially as u havent described any slipping or juddering and loss of drive.
this tends to happen as a sort of limp mode, to allow some movement of the vehicle, im afraid the only option for u is a gerabox specialist.......

Moisture inside the vehicle. If you have a water leak that is allowing water to get into the car it will cause this problem. Also if the A/C water drain is plugged and there is water standing in the blower fan area you will have the same problem.
Pull your carpet back on the driver and passenger side at the fire wall and check for moisture, if the carpet backing is dry on both sides you will want to check the drain under the hood.
Good luck.

check your wheel bearings for excessive play

The first thing I would check is the heater control valve. This valve opens when you turn the inside control to heat and allows hot coolant to enter the heater core. If coolant doesn't enter the core, you don't have heat.

This valve is usually located under the hood behind the engine up close to the firewall. It will have coolant hoses attached to it. There should be an arm on the valve with a cable from inside the vehicle attached to it. This cable causes the arm to move, opening and closing the valve. Have someone inside move the heater control and watch this valve for movement.

During the warmer months, this valve is not being opened and closed, and it can get stuck. Moving the arm a few times will probably get it working again.

should be a seal issue, not mechanical. Is the roof opening/closing properly? If so, while open examine the weatherstripping and look for damage or abnormal wear. with power roofs, sometimes the movement wears down the sealing abilty pending on its usage or debris hiding inside.

It might be that the car has not had the Isuzu factory soundproofing mod done around the gerbox cover - speak with you dealer.
Possibly the alternator bearings are going , an autoelectric shop can tell you .