Yes, you can move a registration to a new machine. Think about it: you bought the license to use the software. It's registered to you, not to the particular hardware. What if your machine got a virus and you had to start from scratch? You re-install all your old programs, and the license gets transferred to the new machine. In fact, you can usually install on multiple machines at once; the limits are (usually) on how many installations may run at once and frequently that number is one. So you can have the same license on your desktop at home, your desktop at work, and your laptop - as long as you use the program on one machine at a time.
As for buying new software cheap - I do it all the time. Best way to buy Adobe Acrobat, or Quicken, or any of a number of other programs, is to go to eBay and find a NEW, REGISTERABLE copy (that bit is the key) of last year's version (or the year before, or the year before that). Example: Client needed QB, but also needed cheap. Told her to go to eBay and buy a two-year-old new copy of QB desktop; this year's version was hundreds of dollars, the two-year-old version was less than $100; she was thrilled. QB old versions - even brand-new - sell cheap because they stop support for payroll after three years, and sometimes the bank feeds won't work. Well, she doesn't have a payroll; not an issue for her - and some of the bank feeds won't work with brand-new versions, depending on the bank - but almost all have web connect download files available, so do those instead. Heck, I still have (on an older machine) and installation of QB2007 that I sometimes have to pull out for one client's file. It works, they do payroll through a service, why pay for a not-needed upgrade?