I'm recording Nile's Annihilation of the Wicked song, and I'm trying to get their sound, but with my amp and guitar (Spider III 15 and ESP f-50 with standard ESP pickups) the high notes in the gallop riff, the second intro, I guess, aren't coming out, they just splutter and die after maybe 2 seconds. How can i get those notes to sustain longer? Keeping in mind there is no sustain knob on this amp.
Compression will help sustain a little, however with your current gear it's unlikely you're going to get great sustain.
What DAW are you using to record? Also, what are using to record with? (i.e mic, interface?)
I'm not sure what a DAW is, but I'm plugging the amp directly into the computer's mic input, and using Acoustica Mixcraft as software.
You're really not going to get a good sound with your setup. A DAW (Digital Audio Workstation) is something like Pro Tools or Cubase. I've never used Mixcraft, so I can't help you there, sorry. If you're wanting to make better quality recordings look into buying a semi-decent interface, there are plenty around and many recommendations on this forum. Do some research, google is your friend.

Sorry I couldn't be of more help.