Battery light is on and heater is out after Battery

Sounds like you connected the battery backward the first time. You better not blame Costco for that. The positive post is always larger in diameter and has a huge plus sign next to it. A number of fuses will blow to protect their circuits and computers so check them first. Sometimes fuses blow when reconnecting a battery or from jump-starting from the current surges when no other problem exists. Simply replacing those fuses is all that's necessary.

When you say the car turned on normally with the new battery, do you mean the dash lights turned on or do you mean the engine started and runs normally? If it runs properly, that proves you didn't damage the Engine Computer. Wiper and fuel pump motors can handle a battery being hooked up backward but they won't work properly.

If the first new battery was hooked up correctly but it was discharged, strange things are going to happen too.

I'm concerned about your last sentence. By "battery rod" do you mean the hold-down bracket? The battery cable clamps should not be touching that but no harm will occur if the negative one touches.

Oops. Forgot about your battery light. Use a grounded test light or voltmeter to measure for voltage at the large wire bolted to the back of the generator. You should find full battery voltage there all the time. If you find 0 volts, look for a large fuse bolted into the under-hood fuse box. It takes a real lot to blow him, but hooking the battery up backward will definitely do it. There are six diodes in the generator. They are one-way valves for electricity. Those diodes block current flow from the battery when the engine is off, but they become a dead short when the battery is connected backward.

Small fuses have two holes on top where you can stick the probe for a test light or voltmeter. You're looking for any fuse where the test light lights up on one point but not the other one. The slow method involves removing each fuse one at a time to visually inspect them. If your fuses are labeled with the name of the circuit, look for one labeled "heater", "fan", "HVAC", or something like that. No sense wasting time checking fuses for things that are working.

There will be two places to look for fuses. Small ones will be used inside the car. Large and small ones will be found in another fuse box under the hood. Common places to find the fuse box inside the car are under the steering column, in the glove box, and behind a removable cover on the end of the dash. You have to open the door to get to those on the end of the dash.

Many large fuses have a see-through plastic cover. A blown one will look different than the others, and it might be black in that window. The generator fuse is usually bolted in to insure a good electrical connection because it has to pass such a high current. The fastest way to check it is to test for voltage on that fat wire bolted to the back of the generator.

To change subjects for a minute, it was normal for your old battery to run dead from sitting for four months. Because of all the computer memory circuits, there is a constant drain on the battery. Unless specified differently by the manufacturer, the industry standard is a maximum of 35 milliamps, (.035 amps). Chrysler guarantees their engines will start after sitting for three weeks with that much drain. The battery won't last four months.

Once the battery is fully discharged, the engine will start with a jump-start, but it can take ten minutes or more for the acid in the battery to become conductive, THEN it will begin to recharge. The recharging process slows down a lot at idle too. You would have had to drive the car at least 20 minutes to charge the battery enough to crank the engine the next time.

Consider yourself lucky too that you don't have a Volkswagen or General Motors vehicle. Once the battery is disconnected or run dead, the engine will not start on many of them, and those that do will not come out of park and will not increase engine speed when you press the gas pedal. They must be dragged onto a flatbed truck and hauled to the dealer to have them unlock numerous computers. Hyundai doesn't design that nonsense into their cars. In my opinion, they are the most customer-friendly manufacturer in the world.