The question says:

Why should I believe that there is such a thing as a God?

Should is the word that stands out to me, I believe that one makes ones own mind up, and there is no should or shouldn't, If you live your life doing unto others as you would have done unto you and in a thoughtful and peaceable manner I dont think it matters if you believe in God or the Great green man from Mars.

I personally do believe in a god, maybe not the difinitive one in the bible - but that doesnt mean anyone else should!
( I also believe in fairies!)

Cheers, Lucy