Here is the item again:
Searching travel websites (A)
to compare room and flight rates,
(B) Shaquita fantasized about
a spring break vacation to Hawaii.
(C) As her unfinished algebra homework
lay ignored on her desk.
You correctly realized that the period after Hawaii created a fragment. As her unfinished algebra homework lay ignored ... is a subordinate clause, so it cannot stand alone as a complete sentence.
To fix this fragment, you chose to do this:
Searching travel websites to compare room and flight rates, Shaquita fantasized
about a spring break vacation to Hawaii as
her unfinished algebra homework lay ignored on her desk.
You have correctly employed Punctuation Rule 1:
Main clause + Ø + subordinate clause.
Rock on!