Even new batteries can be bad so don't rule that out. Jumping it could tell you if your battery is weak. Careful tho, if it's a battery terminal issue then just hooking up a jumper cable can cause it to make enough contact to start and you'll mis-diagnose the problem.

If your cable clamps are loose enough to turn, then I'd say that's the source of the problem. I put some quick disconnects on my daughter's car & they caused all kinds of problems.

You can use your jumper cable to go from the positive lead on the battery to the large terminal on the starter to see if it's a cable issue. After that, you can use it to go from the negative terminal to the engine block to see if it's a ground issue.

From what you've said so far, just put on new cable clamps at the battery & that should fix your problem.