Need help central heat (gas) unit won't stay on!

This is on Trane model YCC042F1M0BB gas heat and electric A/C. I have a LUX programmable t-stat. This unit is not heating up to the set temperature. Sometimes turning the switch off then back on will make the heat come on. However, the one time that I timed how long it stayed on it was about 12 minutes and it still wasn't up to temperature. What are the symptoms of a bad heat exchanger (heaven forbid)? I seem to remember hearing there was a particular sound you could hear coming from the unit if this was bad? In the event the unit has to be replaced (which we will probably move in with my in-laws because we can't afford a new unit) what brand/model would you recommend to replace this? The house is about 1880 sq feet all one level.
Thanks for any and all opinions!
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I had the same problem with a Lennox furnance. I called the Gas Company Service Department. It turned out being a flame ignitor sensor. $14.00 for the part and $80. for the service call (no charge).. The reason I used the Gas Company is that I have a service contract with them and don't get charged on covered appliances. and I trust them more than I would an Independant contractor.

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Thats not one..

Not on that unit, or any unit any longer.

Ok..you can cut the power, and it fires back up....give you a hint...and its in all seriousness....you are controlling a better furnace with a bottom barrel mad eas cheap as they get thermostat. If you want to prove its the stat, do this: First, dont blame me if you screw up and fry a transformer..you do this at your own risk...we replace many a transformer a week for people that cross the wrong wires.. Turn the stat OFF. Take it lose from the wall, leaving the thermostat wiring intact. Find the R, and the W terminals. Take a jumper wire and connect the R and the W terminals ONLY. Time it running and see if it wont run as long as you have the terminals jumped.
If this is the case, break down, and spend a few dollars on a decent thermostat...Honeywell, or Robertshaw.
This is a VERY common complaint with Hunter and Lux stats. What happens is that the thermostat relays simply either quit after a bit of currents been passing through them, or, the thermister that they use to determine room temp is so far out of calibration its not funny.
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Wow, very good. A straight answer.
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its
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You understand what FO means?
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