I remember being able to play 1.09 Diablo 1 under Vista 64, but never tried getting online with it. Diablo 1 is an old 32-bit application made for Windows 95. You could try running the game in some of the compatibility modes that Vista provides but this is an unsupported OS for Diablo 1. Also keep in mind that there is no IPX protocol on Vista so you cannot do IPX LAN games.
Good news, I got it working!. Pretty stupid of me but after an install from the disc, and an attempt to go online without avail I never thought to manually download the latest patch. After getting 1.09b it worked perfectly!