Until you threw the dishwasher problem in there, I had an idea. Now I'll re-group. "The faucet is an old single handle type." Seen this happen many times with these. Look under the kitchen sink area for some type of cut-off valve for the hot water, hopefully there is one. IF there is one, and you can handle this: cut the hot water side valve off, then remove the line that attaches to this valve. IF this is a chrome plated copper line be very careful that you don't bend it any more than necessary to remove this line. Now, using a small bucket, a catch pan of some type, SLOWLY open the hot water supply valve to see if any water will come out of it. Please open slowly so as not to spray water all over the place. If water will indeed come out of the supply valve then your faucet probably is the problem. This will require having to take the unit apart to replace parts and it sounds like this is not your area. Now on to the dishwasher: how does the water line to the dishwasher connect to any and what water line to supply the dishwasher? IMO it should be connected to your hot water supply line in some manner, either the supply tube to the faucet (not my choice) or to the hot water supply line as it exits the wall or floor (my choice). The fact that the dishwasher shuts down indicates that it may have a pressure switch for the water and shuts the unit down because there is no water hot or cold coming in. Now I'm really confused as to how the dishwasher supply line is plumbed up. We need more info on this one, particularly on where the dishwasher is getting it's supply of water. Get back on this please. David