There are a few other big problems with the standard model, but nonetheless, it is still an incredibly successful theory, and the Higgs Boson is an incredibly important part of an incredibly successful theory.
Even outside of the Standard Model, the Higgs Boson is a fundemental aspect of many theories that attempt to describe our universe on the small scale. The LHC is guaranteed to have an incredible impact on our understanding of the universe, regardless of whether or not it finds the Higgs. If it doesn't find the Higgs, it blows a huge whole into the Standard Model (because it means that either the Higgs doesn't exist, or at least gives us a good idea of it's energy (which tells us other important things about it). And if the LHC does find the Higgs, then we've just experimentally verified the origins of mass itself. This will affect every single other theory out there in some dramatic way. Also, it would be the only spin 0 boson in existence, which by itself makes it very interesting to theorist.
Actually, that pretty much is all they're doing lol. But, as in Eliseos' example, if the only way to understand watches were to smash them apart and see what pieces come flying out, then we really have no other choice.