In Beowulf, what does Grendel want to do? What is preventing him from doing it?
I believe Grendel is really undecided on what he wants to do. The poet tells us that he is a descendant of Cain who has been banished to the swamps and dark places by Lord for his murder of Abel. Thus, I think that on one hand he is jealous and really wants to join the men of the world, but can't since he has been placed where he is by the Lord who banished Cain. Since he can't join them, he cannot stand the sound of the music and enjoyment that he hears each day so he wants to destroy them. I believe he is limited in his ability to destroy because it seems he cannot go far from his lair and maybe cannot be out by day. Furthermore, he might not really want to destroy Hrothgar's people entirely, he may just want to keep them from enjoying the mead-hall at night. In this he is successful for 12 years until Beowulf comes to Hrothgar's aid.
Grendel primarily wants the noise coming from Hrothgar's hall to stop. He is bothered by the cacophony and its implications of men having a good time (he is miserable in his watery lair.)
There is not much preventing Grendel from achieving his goal until Beowulf shows up. He snarks down warriors like they were Cheetos. But when Beowful does come to rescue the kingdom, all bets are off. The terrifying Grendel has met his match in ferocity. He will be defeated by the great warrior, and his arm will hang above the hall (claw and all) as testament to Beowulf's prowess.