I'm on the 3rd level of the vault of the Cathedral. I've chosen to just blast my way through and yet...I come to a locked door in front of an elevator. All of the info I see online says to pick it. Well my lockpicking skill is like 15% and I keep trying but it doesn't work. I've tried dynamite, plastic explosive, I have an electronic lock pick but it doesn't work either. Am I just completely screwed?

You're not. Took a look at a walkthrough, but still can't remember the specifics though, so I can't remember exactly what to do, but in any case there's no high skill requirement there. Maybe it was one of those doors that requires a badge/keycard or something. Or there's a hidden lever or something. High lockpicking skill is not a requirement anyway, even if a high skill might give an easy workaround.

You don't have to go down, what you seek is hidden somewhere on that level.
If you insist on exploring the lowest cathedral level you need 57+ lockpick skill and electronic lockpicks, so you'll have to gain a few levels first.