If your other primers fired it may be a matter of not having seated that one hard enough. They like the anvil compressed into the priming mix by about three thousandths. Check your firing pin protrusion.
As others said, soaking is unpredictable. Some primers are killed by it, but most seem pretty impervious to that action. Eye and ear protection and just press it out. If you suspect the case, it is worth the investment to seat another primer and be sure it is in place solidly and firmly, and try firing it. If it goes, the case is not at fault.
It would be unusual for a standard full-length seating die to make a fired case shorter than it was coming from the factory. If you have any factory new ammo or cases, you might compare the shoulders. If you don't have a comparator but do have a caliper, you can just pick up a spacer to put over the neck at Lowe's or Home Depot with a hole the touches near the middle of the shoulder. Measure the combination of the new case and shoulder from case head to the top of the spacer, then repeat with your suspect case to see if it is actually shorter. If not, it was entirely a primer issue; either inadequate seating depth or a faulty primer.