Relic Weapon Quest

Is it possible to have my relic quest chain pick up where it was abandoned?

If you abandon the quest then no. They are very clear about this when you undertake your relic quest.
You can only have one relic quest at any given time. If you want to switch relic quest you have to first either complete the old one or abandon it but in doing so you will lose all progress.

I must have missed the very clear part, but still it wasn't abandoned intentionally. If it's the case that I can't continue my quest from where I left off I'm too dumb to be playing this game and will no longer do so.

How do you mean not intentionally?
Also, I was not trying to be rude, just informative.

I understand that you weren't, I'm sorry if I came off as offended by your comment, just flustered with my own ignorance of the mechanics of this quest, and if they're this unforgiving this isn't a game for me; I went to the part of the chain unlocking the Hydra event, I didn't realize that I'd be ported into the encounter. Once I was in there by myself I thought abandoning the quest would port me out, it didn't. So, abandoning the quest was intentional, but the outcome wasn't what was expected. Abandoning the quest only to restart it wasn't intentional.

outch, that sucks indeed.
Your best bet is to try support but I find it hard to believe they will help you honestly :(