The grill does not work

There are 3 areas that most often fail, I will list them in order of most common to least.
1) Most common is a failed element, in your case, the inner one. These are replaceable, but the job is not easy, requires taking the oven all apart.
2) There are wires inside the case that go to each element, and once in a while they can "burn" off or fail. Again, big job, but doable.
3) The switch on the oven could be at fault, internally. Rare, but it can happen. Easier than the first two to fix.
God bless your efforts.

Not familiar with these models, but it sounds to me like it could be a gas pressure problem...? Is there a regulator - sometimes they fail. Are any other appliances hooked into the same gas line? If so, how well are they functioning?

First things first. The top oven lights ONLY come on when the top oven is switched on. Operating the grill DOES NOT turn the lights on. If you wish to see what you are grilling, you have to turn the top oven control knob on to its first position as well as turning the grill on.
Secondly, the grill only works when the door is open. The grill does not work when you shut the door. When you open and shut the door, you should be able to hear the microswitch operating. It is located in the right hand side of the cooker, between the inner and outer panels - you cannot see it. I haven't seen the switch first hand but they normally come with an arm that contacts the door mechanism and the door mechanism operating, causes the arm to move, which causes a button on the switch to move and make the circuit. It has been known for the arm on the microswitch to bend with use so it no longer works correctly.
If you have checked all above and you hear the switch operating, then it could have failed. They are quite common, so if you can't get one from STOVES, try espares or someone like Maplin or RadioSpares.
The get to the microswitch you have to take the oven out of the housing and then take the right hand panel off. You should then be able to see it and check its operation.
All the best

If this is a propane grill, try replacing the regulator and hose going to the tank. When a regulator is failing, it allows gas to pass, but not enough to allow the grill to heat up properly. If this is an older grill. You can also check each burner for blocked gas ports. Just a few blocked ports in a burner can prevent the burner from lighting completely, or from moving from one side of the burner to the other.

More than likely the grill element has failed, if the element light comes on, then I would go for the element.
If no light, then probably the grill switch is faulty.

if the burners are fairly new , not old and full of rust, yes, it is the regulator if you are using tanks.

You will probably have to replace the electronic ignition module located directly behind the panel the button is mounted on.

Contact a retailer for replacement parts, as they may carry the module.

All else fails, you will have to contact the manufacture.

The grills appear to be independant of each other. Does the oven still work and the oven light come on?

Depending on your answer it could be that the Top Oven Switch has gone faulty. The Grill Regulator and the Switch work together on the top oven. To get at both you will need to take the top of the oven off.

check for a failed heating element