You got the right idea, just substitute your new desktop for the CD recorder!!
You could either take the line outs from your recorder to the line in on your soundcard, or, if your soundcard has a digital input you could use that if the formats are compatible (the Boss probably puts out SPDIF?) and if your soundcard will support it. That might be something to look for in your new desktop- make sure it doesn't have onboard sound (or that it can be disabled if it does) and then drop an MAudio 24/96 Audiophile soundcard in there. If you not too picky about how things sound, a good Sound Blaster will sound ok.
Either way, once you get the mix into the computer, you want to master it. I have always used Sound Forge for this, and it's always done the job well for me. It's not cheap, but it is very versatile. It can also handle your CD burning requirements. There are others out there, but this is where my experience is.
Where you at in Atlanta? I'm up in Woodstock.......