Having just worked on the Suburban SW10DE just recently maybe I can make some suggestions. When you turn on the inside switch it will try to start the gas water heater three times and then shut down. To re-start this cycle you need to turn off the inside switch for about 10 seconds and then turn it back on and it will go through the three tries again. So so far this is working properly. However, if you are also running it on electric heating the water may be hot enough that it doesn't need the gas flame to heat it more. So it locks out. So to really test this is to leave the inside gas switch off for awheil and also turn off the black toggle switch(on the bottom front of the water heater behind the water heater cover) that turns on the electric heating side of the water heater. The let the water cool off or run the hot wter faucet for a period of time until the water in the waer heater tank cools off significantly. Then turn on the inside electrical switch that turns on the gas side of the water heater. I suspect that it will then work the way it is supposed to. Now if that doesn't work, try resetting one or both of the two reset buttons covered by a black runbber membrane on the front of the water heater that is the 12V high temp limit thermostat. To reset these the water temperature must be under 110 degrees F. One is a thermostat hi-liit for gas operation, the othr is for the gas system. The key before you do any more testing or resetting the buttons is to turn off the 120V side of the water heater and let the water cool below 110 degrees F before you try heating with gas again.
Then if none of these solves the problem you will need to check if you are getting an adequate gas pressure to the water heater. There is a possibility that you may have changed tanks recently and allot of air is in the lines to the water heater and it may take a few cycles of the gas side starting cycle to clear the air out. I have found though that if you run the burners on the stove for awhile before trying to start the gas side of the water heater it will usually light during the first three tries. But if not, turn the inside switch off for 10 seconds and try again. This starts the three starting tries over again. I suppose it is possible that you have a lockout on the gas lines due to a sudden pressure change by changing tanks and turning them on too fast. to test for this problem, turn both tanks off and wait 5 minutes. then turn on each tank very slowly and then check to see if you are getting a clear green indication on the auto switchover regulator indicator. If either or both lever positions show red then the overflow lockout valves have locked out or are limiting the gas flow to a much lower pressure level. A way to check to see if the gas pressure is being limited try lighting the three gas burners and if they light then light the furnace. If the furnace lights properly w/o a reduction in the three stove burners flame height then a lockout has not occurred. To learn more about these lockout issues check and read the application info at:
http://www.shleggitt.com/edlees/
I suspect one of the above checks and corrections will get you going! If not provide further info on what the symptoms are.