Okay, long story short, I'm self-taught and I can't find a teacher, so I came here next.

Been trying to play Metallica's One, and I just got my first Elec. guitar and a solid amp. The only trouble is, I can't get the sound to "stay" long enough to play the hammer-ons and pull-offs required in the later solos (15 and up). I get a single squeak, then it's silent. And I have a feeling this will become a problem later on, so any help would be greatly appreciated.

Merry Christmas and God Bless!
You guitar isn't set up very well, so you're fretting out high up on the neck. Raising your action might help, but if this isn't a very good guitar, it might not help much.
Dean MS STD V w/ Dimebucker
Dean ML '79
Jackson DKMGT
Randall RG75
Peavey Bandit 112
Boss NS-2
practice hammer-ons and pull-offs :P
just practice until you feel comfortable with it. look for some exercises in the lessons part of UG or on youtube :p
Beer is fine.