RV Repair: Furnace, Radio and light, furnice, marine battery

Question
I recently purchased a 1985 Jayco trailer. The furnace I was told would not work. the first time i used it worked fine for 3 days  went back 2 weeks later used it  started up fine  but seemed to loose power along with one light over the sink and the built in sterio system.  They are all on the same side ot the camper.  The furnice  is a subberban model NT305  and Serial number 1529433.
I am guessing since the sterio and the light over the kitchen sink went out they may have somthing to do with each other maybe a faulty wire or somthing. What can i do to check to see where the problem is?  I am out in a resort with no way to haul it in to a repair place at this time.  Is there any place I can check to see if its a faulty wire?  I have checked circute breakers and they are all fine. We have a Brand new marine battery hooked up.  Has a new converter.  The furnace, light and radio worked perfectly after sitting all winter but the furnice did not work when they stored it away. I could actully see when the furnaice was running, the light started to dim  and then the three items  just  died.   All other  outlets and  lights  and every thing work fine.   The Anttenna  doesnt work either  but not sure if thats just because its never been used  and has been corroted or  if the little power booster isnt working  along with the other things.  again on the same side as every thing else.   I appreciate  any info you can give me.

Also is there a good product out there i can buy that i can tell if there is a leak of gas anywhere. I get a little nervous.  If  we do not light the pilots in the oven and on top of the sotve  It willtend to smell gas is that normal?  I had a small camper  previous to this and we did not have to have  pilots lit on oven or stove  and there was no gas smell.

Thanks for your help. this is Monday 22nd And will be leaving for camper on May 26th.  Hopfully you will be able to help and i can take care of it when i get there firday.  

Answer
Hi Lorraine:
You are going to need a voltmeter to check this out. With a 20 year old trailer the wires may be corroded to the point that the voltage to the things that are not working is low. The furnace will work down to 8 volts or so and then quit. The radio and light will work to a little lower but not much. I would start checking voltages at the battery and then work closer to the individual device to see where the voltage problem is. Hook the black leads of the meter to the negative of the battery and the red lead to the positive. If you find low voltage at one point work back to where you had good voltage to find the problem. It could be anywhere. Trouble shooting electrical problems, especially low voltage can be frustrating and time consuming but it is the only way to fix things. Good luck.
Bill