In Beowulf, although the Danes are portayed as men who have faith in God, what pagan rites suggest their desperation for help in their struggle with Grendel?
As your question suggests, Hrothgar and his men, who have been brutally attacked and beaten by Grendel so often that they have to abandon their celebration hall, Heorot, are so desperate for help that they resort to their pagan beliefs--despite the fact that they most likely have been Christians for several generations:
Sometimes at altars they made offerings/to pagan idols, and prayed aloud/for the spirit-slayer to send them help/for the people's distress. (ll. 175-178)
Even though the Beowulf poet makes it clear throughout the poem that the primary belief system of Beowulf and the Geats, and Hrothgar and the Danes, is Christian, it is also clear that their earlier pagan belief system is still an important component of their religion. Notice, for example, how often the poet refers to God and Fate (or Wyrd) within a few lines. If we keep in mind that we are reading about a group of people who are still in transition from paganism to Christianity, we can understand how, when they are under incredible stress, they might revert to their earlier religion.
Even as he recounts the Danes' reversion to paganism, the Beowulf poet points out the serious error the Danes have made in appealing to their old religion:
. . . they didn't know the Maker . . . they didn't believe in Captain God,/nor know how to praise the Heavens' Protector. . . . (ll. 180-183)
In other words, to the extent that the Danes call upon their pagan gods for help, they are wasting their time. To make this clear, the poet tell us that Hrothgar is "unable to ward off woe; that war was too fierce" (ll. 190-191), a clear indication that, if help is to arrive, it is not coming from pagan gods.
These lines point up one of the most interesting aspects of Beowulf--a picture of a society in transition from its original pagan belief system to Christianity. The fact that the Danes seek help from their pagan gods is not so much a rejection of Christianity as it is a desperate plea for help from all their gods, the old and the new.