Without knowing what OS you're talking about, it's impossible to answer this question.
Assuming Windows 2000/XP, as long as the same HAL and disk controller driver can be used for both the "before" and "after" cases, you should be good to go.
The OS is totally ignorant of the case. Moving the hardware to a new case will not require a reinstall.
A new processor won't require a reinstall in any cases that I'm aware of.