Covariates, interactions and constraints all together does make for a hefty model. While a new machine would be helpful, I wouldn't expect monumental improvements.
Most people automatically assume that faster processors will make the most difference, and they end up trading off some things like the hard drive and RAM. You should get the fastest processor you can for your budget, but not at the expense of your hard drive or memory. HB is not multithreaded but does benefit indirectly from multiple cores (4-8 cores should be sufficient). In HB the speed per core is more important the number of cores.
HB is I/O intensive, so having a fast hard drive can be very beneficial. SSDs are much faster than conventional drives, and can help a lot over the 5400 rpm drive you have.
Adding as much RAM as your budget allows will help keep the system from thrashing, which is where the operating system swaps between hard drive and memory constantly. This can kill HB performance.
I wrote an appendix in the CBC/HB manual which describes some of these issues in more detail.