The control knob of my Colemans Hot Water on Demand Model #2300-70 doesn't turn at all. How do I repair this?

how is it going to heat the water without propane ?

Hot water is gravity fed through your pipes. When you turn the faucet on the water will flow through the pipes. If your hot water heater is natural gas driven relight the pilot. Same if oil fueled. If electrical, check fuse to see if it has blown or the circuit breaker has tripped. If either has tripped, replace it and if it blows again the heater has a serious failure, you might need to buy a new one. If pilot won't light on gas unit, try relighting after 5 minutes, could be a bad thermocouple.

What boiler do you have and is the controller a radio controlled thermostsat

Sounds like it. Before replacing gas control, try removing thermocouple connection at valve and spray electrical cleaner in there and blow out with compressed air after, being careful not to get it in your eyes. If no electrical cleaner, try WD-40 and blow out after. If you twist up a piece of fine steel wool and insert in there as well and try to spin/twist it to clean contact inside may help as well. Blow out goo after and re-install fitting and try again. If that doesn"t work, replace gas control.
P.S. Highly recommend certified experienced tech perform this control valve replacement if necessary.

At the controls there should be a knob that says " Pilot"... "ON" Turn the knob to pilot and hold it down while lighting the pilot lite. Keep holding it down until it gets warm enough that when you leave it up the pilot stays on. Once the pilot lite stays on on it's own turn it to on.

A leaking water heater cannot be repaired, assuming it's the tank leaking and not nearby water pipe.
http://waterheatertimer.org/Water-heater-leaking.html

First thing is to protect your property from catastrophic tank failure where tank ruptures and water runs until it is shut off:
Tanks are under pressure when they are hot.
Close cold water shut-off located above tank.
Turn control knob to 'pilot' so pilot is lit but burner will not turn on.
Open hot side on tub for few moments to relieve tank pressure.

Now your property is safe.
You need a new water heater.
In mean time, gas water heater makes 41 gallons hot water per hour.
Shower used 5-9 gallons hot water.
Bath uses 10-15 gallons hot water.
You can turn on water heater for short stretches and limp by until you get a new heater.

Steps for installing gas water heater:
http://waterheatertimer.org/How-to-install-gas-water-heater.html

will still be under warrent call supplier

You can eliminate the shower control knob possibility by turning on your hot water anywhere else in the house. If you get hot water in other places, then it could be the knob causing it. A substantial lime buildup in the tank can also cause poor heat transfer from the elements to the water.

In most of the tankless water heaters the tempature of the warter is controled by the rate(amount) of vlow of the water passing through the unit. Turn down the flow of water going into the water heater and the water that is still passing through will be hotter. Carefully. A little at a time,so as not to be too hot.  

I found a way to get warm water in the shower, but I'm not sure it qualifies as a solution. After trying everything else I thought that maybe when I was feathering the faucet in the shower toward the cold side so I would get warm water that at a certain point it blocked the flow on the hot water side enough so that the sensor in the hot water heater sensed there was no demand in the line and it shut the water heater off. To test this, I went to the kitchen and turned the kitchen sink faucet all the way to the hot side and then turned it on so that I got a small flow of water. I waited for the water to get hot to be sure the hot water heater was working. Once it was hot, I left it running to keep demand in the line and then I went to the shower and turned the faucet on. When the water got hot I started feathering the control towards the cold side and soon I had warm water. So I think I'm right in that the sensor in the hot water heater was shutting the water heater off when the demand in the shower was lowered to a certain point when I was trying to adjust the water temp in the shower.

So now I can get warm water, but it means I have to leave the hot water running at another fixture in the house to create a false demand in the system so the hot water heater doesn't shut down. Is there a way to adjust the senor in the hot water heater so that it will stay on when I'm using the shower only, so I don't have to waste water by running another faucet when I want to take a shower?