I'm pretty sure the MX-850 can learn from most IR remotes. I have an MX-850 that works for my home theater consisting of about a dozen components, some of whose codes had to learnt.
You should be able to stick the base station's blaster in front of the IR receiver, or run a line to it for better control.
Here are other HTPC IR control solutions that should also work for what you want to do:
http://www.streamzap.com/[Link: soundgraph.com]