What do Hrothgar and his council do to try to save his guest-hall?

In the beginning, Hrothgar and his council are powerless in the face of Grendel's attacks. The guest hall, Heorot, is overtaken by the monster. Grendel prowls the halls at night and leaves a gruesome trail of gore behind him in the morning. Initially, Hrothgar's faithful warriors try to defeat the creature. However, none of them are successful in their efforts. As a result of Grendel's attacks, the guest hall becomes deserted.
Hrothgar and his council are reduced to praying to their pagan deities for assistance.

Sometimes at pagan shrines they vowed / Offering to idols, swore oaths / That the killer of souls might come to their aid / And save the people. That was their way, Their heathenish hope; deep in their hearts / They remembered Hell . . . Oh, cursed is he / Who in time of trouble had to thrust his soul / In the fire’s embrace, forfeiting help; He has nowhere to turn.

The king and his people believe that only "the killer of souls" can defeat an obviously malevolent creature such as Grendel. We do not know who this "killer of souls" is; a close equivalent would be the Canaanite Moloch, an ancient demonic deity or fire god. In the passage above, the writer laments that the heathen must "thrust" their souls into the "fire's embrace" during a time of extreme need. In ancient times, people who worshiped Moloch consigned their firstborn to fiery deaths in order to secure the blessings of life and prosperity.
Before Beowulf (Hygelac's thane and the son of Ecgtheow) arrives, Hrothgar and his council do little more than pray to their pagan gods to save their guest hall.
After Beowulf's arrival, however, Hrothgar decides that Beowulf is the Danes' best hope against Grendel. He eventually makes Beowulf the "hall-warden" and entrusts Heorot to his care.