While you're goal is noble, a new computer won't really mean that he can produce better quality music. Digital music just doesn't really work that way. And your average low to medium cost computer is likely going to be of rather poor quality such that it's likely to just be an act of frustration. If you can't spend at least $1,000US on a desktop or about double that for a laptop, it's really not even worth bothering for any kind of regular use.
What you could maybe do, is spend some time asking your son some questions, try and feel out some things that seem to be limiting him with his current laptop. If he seems to always be running out of disk space, you could go out and buy him like a 2TB external HDD for $150US give or take. Maybe buy more RAM for the laptop so that programs run a bit smoother. If you want it to be a surprise, just spend a week or two just asking him occasional questions to try and get some information on what kinds of things he'd like to do but can't. Then you can come back here and people can give some better suggestions.