Anyone know of a website where I can find Abel's original proof that there exists no general solutions to the quintic equation?
Original Proof ? Do you mean the manuscript ?
If you know German , you are lucky , see
(Papers over the algebraic dissolution of the equations , Abel , Niels Henrik )
Abhandlungen über die algebraische Auflösung der Gleichungen : Abel, Niels Henrik, 1802-1829 : Free Download & Streaming : Internet Archive ( should be the translation of the manuscript )
or if you are a Frenchman , why not see his collected works ?
Vol. 1
Oeuvres complètes de N.H. Abel, mathématicien, avec des notes et développements : Abel, Niels Henrik, 1802-1829 : Free Download & Streaming : Internet Archive
Vol. 2
Oeuvres complètes de N.H. Abel, mathématicien, avec des notes et développements : Abel, Niels Henrik, 1802-1829 : Free Download & Streaming : Internet Archive
Actually , they all come from this page
Internet Archive Search: Niels Henrik Abel
Hope they are useful