Since you said this was old, i'm going to assume that you do not have a control circuit board in your furnace. I'm also going to assume you don't have a really really old milliamp type furnace. So, with that in mind, the first thing to do is make sure you have 120v to the furnace, and second make sure you have 24v coming from the transformer in the furnace. If you have 24v then check the voltage at the gas valve. If you have 24v and it won't open and your pilot is lit and you have the knob turned to on, then you have a bad gas valve - replace it.
if you replaced the t-stat and it worked then stopped, you probably fried the heat anticipator in the t-stat by not having it set properly.
If you have 120v but not 24v, then you may have any of the situations explained below.
if you had the anticipator set correctly but it still fried anyway, then you have a short or a partially shorted situation in your low voltage heating circuit. remove the t-stat and check the amp draw that is pulled from the R terminal to the W terminal. do this check quickly because if a short is present you may fry the low voltage transformer. you will check the amp draw in this manner after every step that follows. It should be anywhere from .02 to 1.5 with around .06 being somewhat the normal draw. if it is within the ranges i stated, check the heat anticipator setting on the t-stat and see if you had it set properly. if so, then get a new t-stat. if the amp draw is high, then disconnect the gas valve and see if the amp draw drops. If it does, then replace the gas valve. If it doesn't then remove the white wire before it goes into the furnace. if the amp draw drops then you have a prob in the furnace. some furnaces have fan controls that use 24v to operate the fan in the heating cycle. it could be this or could be a wire that has chaffed and is shorting against the furnace housing or some other component. trace wiring and repair. if you removed the white wire before it goes into the furnace and you still have a high amp draw, then you have wire problem coming from the tstat. trace wire to find. if the wires go into the wall, you just have to pull new wire.