I'll expand on Randall's reply....
Forget ADAT. Your best bet is to enter the world of computer recording. If you have a reasonably modern compputer running XP you have the choice of several programs and digital interfaces that will give you the capability you need. Here's a few options:
Program: Reaper has already been mentioned but there's another program that's a little more developed and only costs $75. It's called
n-Track Studio and it's very easy to use yet very powerful. You can download the demo version and see if you like it.
Interface without preamps: If you want to get an inexpensive mixer, such as a Mackie 1642VLZ that includes preamps, you can get a straight digital interface such as an M-Audio Delta 1010 that will give you 8 channels for about $400. This is a workhorse of an interface for a very reasonable price.
Interface with preamps: If your computer has firewire capability you can get something like a Presonus FP10 (Firepod) that has 8 preamps for about $400. This interface plus recording software will give you everything you need to record your band.
To get better drum sound you're going to need more mics, more experience, some plugins, and some mixing skill but this setup will get you on your way.