I'm imagining a computer set up for DJing with big-ass speakers on the outside top lid, and a bunch of analog controls on either side of the keyboard, and a heavy battery.

That's not only possible, but was done to death in the early 2000s during the heyday of car audio components, "home theater" PCs, iPods, and finally good enough laptops.

If you built one of those you were automatically the DJ after school, at the skate park, etc. You better believe those SLA batteries were heavy.