Car shuts off when A/c or Heater turns on?

ok, so here are some details to this car, for some background info.

Bought used with 133200 miles on it. It is a 02 chevy trailblazer. When bought it, temp was at about 220-225. Figured it was just in need of a flush and thermostat. Well I had flushed the the radiator, with no thermostat 2 weeks ago, I ran a engine flush solution in it as well it dropped from 220 to 215. The next week I did the thermostat and it dropped the temp to 210 and a little below. no the temp fluctuates ever so slightly with i drive or sit parked. IT does not go above 210 at all. The fan does work and kicks in when it should. I turned the heater on high after the last time, and car just shut off. will not stay on with out the accelerator being pressed down. I drove it, it did stay on, but when i stopped it acted like it wanted to shut off. A few days later I turned the A/C on and it car stayed on, came to a stop a few times it stayed on, then then last couple stops it started to idle rally low at stop then just shut off.

We used the car a few times prior to the work being done, Ran the car with both a/c & heater on high and it didnt shut off. so just wondering why It would be doing this. Any help is appreciated. thanks.

I also did air filter, fuel filter, and plugs. all these were done before the car started shutting off with the AC/heater. They didnt seem to be any effect to it.