Can Loose Battery Terminal Cause These Problems?

It sounds like you have the diagnosed correctly already. That cable clamp should be tightened right away as it's the battery that helps the voltage regulator from allowing system voltage from going too high. Depending on the design of the charging system, it can also allow system voltage to drop too low. At that point computers begin to shut down or do weird things. When they turn themselves off, they turn on their warning lights to let you know.

This can also lead to minor current surges that blow fuses when there's really no actual problem. Once you have both cable clamps cleaned and tightened, if anything doesn't work, start by checking the fuses. I can help with that if necessary.

Here's links to some related articles you might find of interest:

https://www.2carpros.com/articles/everything-goes-dead-when-engine-is-cranked

https://www.2carpros.com/articles/how-to-check-a-car-fuse

The battery is the key component in holding system voltage steady. To get technical for a moment, all "AC generators" develop three-phase output with a waveform that looks like the top one in my drawing below. You won't be tested on this later, but the generator's output varies between 14.0 and 14.5 volts. The battery smooths that out to hold system voltage steady.

When the battery is missing from the circuit, as in a loose cable clamp, it's up to the voltage regulator to do that job on its own. That rarely works. On some car models, the regulator "sees" the 14.0 volts and tries to increase system voltage by making the generator work harder. Even though the result is output voltage rises, the regulator still sees a voltage that's too low, so it keeps on and keeps on raising generator output. Under the right conditions system voltage can go higher than 30 volts. That will damage computers and burn out any bulbs that are on. One variable in that list of "right conditions" is engine speed. All generators are very inefficient at lower speeds, so that's where less damage is going to occur.

On some car models, the voltage regulators respond to the high points on my waveform, 14.5 volts in this case. In response, they try to lower system voltage. There's a limit to how much control it has, so even though system voltage does go down, the regulator still sees the high points on the waveform, and it keeps on trying to lower the voltage until it's so low, the electric fuel pump, injectors, and electronic ignition begin to shut down. Generally this doesn't cause damage to other parts, but the engine will stop running or it will run very poorly.

1987 and newer GM vehicles have generators well-known to develop harmful voltage spikes. The battery must be in very good condition to dampen and absorb those spikes. When it gets old or has a loose cable, it can't clean up those spikes. Those spikes can damage the generator and interfere with computer sensor signals. That's the extreme case.

Regardless, we know a loose cable is going to cause something unusual to happen. The hardest thing in their life is running the starter motor. If the engine cranks at a normal speed, everything else should be fine.

You're welcome. It's surprising there weren't more symptoms or more warning lights.

Please come back to see us with your next problem.