Van won't start, bad relay? short circuit?

i have a 2005 Town & Country that now won’t turn over. When I just turn the key to the on position (not even to start) the gauges flip around, the odo flashes intermittently as if there’s some kind of short, and i can hear a regular, repetitive clicking from an area behind the battery that sounds like an electrical relay of some sort trying to engage but failing. Short history that may be related: I recently replaced the blower motor resistor since the AC blower would stop after about 10 min of driving. (Btw, replacing the resistor worked for a while, then failed again, so something else is going on). I had disconnected the battery when I replaced the resistor and then 5 days later the car wouldn’t start. It’s 2 year old battery, so I assumed there was corrosion on the terminal and I had not reconnected it tightly enough. At that time, a quick jumpstart got it going again. A couple days later, it wouldn’t start again, would only “click” when turning the key (e.g. starter solenoid). Now, it won’t even do that, just this repetitive relay sound and the “short-circuit” appearance on the gauges/readouts. Ideas? At least it’s in my garage!

Sounds like you have a bad battery or at least a battery that is run down. That clicking is because the battery can’t deliver enough power to turn the starter but just enough power to turn the starter relay on. The voltage drops when the starter tries to turn and thus the relay drops out. Since you have the key turned, the battery is unloaded so the voltage is high enough to turn the relay on and the whole things starts all over again.
Long story short: It may not be a short.

Have you tried charging the battery?
After it starts, what’s the voltage across the battery? Have you looked at the battery connection to the frame? That could be a bad contact and would look like a dead battery as well.
It could be that it isn’t being charged properly, pointing to the alternator or related issue. Or perhaps something is draining your battery even with the key off.

You need to clean the battery terminals/posts and test the battery to begin with.

The reason the resistor failed is probably because of a worn and dragging blower motor. A failed resistor is generally a symptom of something, not a cause.

Try a chargeing system test at a local chain store. It is often free. The alternator may not be keeping the battery up. Also bad battery-starter wire connections. I have seen my own battery fail due to low volt cranking killing the plates inside the battery. Under low volt they tend to heatup and warp. This is bad and causes a cell or two in the battery to fail under load but look ok to marginal with a meter test. Your issue with gauges suggests that the battery is not good underload. Check the volts while you use the horn or any device that pulls current like the headlights. Even the chain parts stores could help you with this test. If the battery is bad make sure to go to someone who will give you a trade in value.