I will be try to be exact as possible.

1990 Ford Ranger 2.9L 4x4.
Was running a few weeks ago. Now wont crank over.
The battery looked like it threw up and choked on its own vomit.
I bought a new battery and hooked it up.

With the key in the ignition and turned in one click, the dash lights and gauges will turn on. Upon turning the key to Start. I will hear a single loud click from under the hood. The dash gauges will immediately turn off and no crank. Turning the key again will show zero response from the dash lights and gauges, and when turning it to start there will not be a loud click anymore.

My semi educated guess is that there is an electrical breaker of some sort that I am triggering.

Could you help me solve this problem?

 

To all those future lurkers. I have solved the problem.
Magic!

I imagine the loud click was the starter solenoid refusing to power the starter.

I just kept trying to jump it and eventually got it going.
The alternator is iffy with this one.
Lots of lights that stay on for no good reason... black magic.

 

Sorry I missed this the first time.

Yes, on many systems when key is turned to START the ignition switch cuts power to everything except engine systems, so it is not unusual for dash lights/gauges to shut off, this gives all available battery amps to starting engine.

Yes, the loud click would probably be the starter relay(if on the inner fender) or starter solenoid(if on the starter motor), not sure which one the '90 uses.

This "click" means relay/solenoid moved but if starter motor doesn't start turning then it is either bad or it isn't getting enough amps via relay/solenoid or battery cables to starter motor, don't forget to check Ground cable, it is just as important, if not more so, as the 12volt cable
The relay/solenoid "click" is a different electrical circuit and requires very little power, under 1 amp.
Starter motor needs 200amps

Car battery's last 5-7 years but from your description it reads like the voltage regulator in the alternator has failed.

So new battery will suffer the same fate if that is not corrected.

New battery should have 12.7-12.8volts with key off
After starting engine battery should show 14.5volt-14.9volts, approx. 2 volts above battery voltage(key off), above 15volts means "Get it fixed right away"
This is the Recharge voltage
This should last a few minutes, then battery voltage should start dropping
After 5 minutes of engine running battery voltage should show approx. 13.6volts
This is the Maintenance charge, approx. 1 volt above battery voltage(key off), this keeps the battery charged but won't cause it to "boil over", what you described.

These voltage changes are done by the voltage regulator in the alternator.
If your battery voltage stays high, above 14volts, then your new battery will get "cooked"