Nope. Don't have the required runes for the unlock door spell.

Did you plant the silver seed? If so you could probably starve yourself to death, get reincarnated and escape that way.

Never found a place to plant it, or figured out how to plant it.

It's just use-target. The main limitation is that it can't be too close to other objects/walls. It has to be planted in appropriate terrain, of course.

Check the clue book about opening that door from the inside. I'm sure there is a way but I don't have it handy right now.

Do you happen to have a scroll of Gate Travel on you? That's one sure way out, unless the moonstone was brought in the room with you. The first one is available on dungeon level 5.

If you have a lockpick you can try picking the lock, but that doesn't work on a lot of quest doors.

Apart from that your best bet is probably to use a character editor to do one of these:
1. If you have a lockpick, give yourself 30 lockpick skill (may not work on some doors)
2. If you are at least level 9, give yourself the "Ex" and "Ylem" runes for the Open spell
3. If you are at least level 11, give yourself the "Vas", "Rel" and "Por" runes for the Gate Travel spell

Think I'm just gonna go ahead and move on to UU2. Everybody tells me that's the better of the two games.

Then everyone's wrong.

Got stuck in Underworld II as well it seems.

My only save file has me dying of poison with about 15 health left. I don't have the necessary runes to dispel poison and I'm out of MP. No restorative items left. Sleeping kills me.

Do you have any potions? There are curatives and healing potions are semi-common.

Depending on where you are it might be possible to make a mad dash for a certain plot object.

Do you only use 1 save file? That's pretty harsh, especially if you're going to save while poisoned! I wouldn't really call that getting "stuck" though. That's just an unfortunate event.
I'd say raid the castle, even if you have to steal someone's potion. There might be a healing or curative lying around in someone's bedroom. Nelson has chests, which might have potions. Can't remember exactly.

Well, after your experiences with the shrine room in the troll area of UW1 I would have thought that you wised up and used several save files now. I guess some people never learn.

I didn't want to end up save scumming the game.

I definitely understand. But it's kind of ordinary for old games to be brutal. It's not like Oblivion where you're assured relative safety, no matter where you save.
I usually use a main save, then a test save for when I think something might be going permanently wrong (ie. imminent death, upsetting a major character, missing an unrecoverable plot point). Then I can just go "Whoops, I'm doomed. No problem, though."

I recommend saving whenever you enter a new level in UW and a new world in UW2.

But on the other hand you can always restart the game when you shoot yourself in the foot, if that makes you feel better.

I recently tested that out. I had 5 skill points and spending them on Syria increased my sword skill by 8 points. Spending them on Lobar increased my sword skill by 11 points. So Lobar statistically is the better trainer. I had just never figured that out, because usually I only train once or twice.