I'm not a forensic specialist, but I did spend some time researching the field because I also thought it would be interesting to get into. Personally, I would removed the drive and use a forensic write block to ensure that absolutely nothing can be written to the drive - and more importantly, that no one else can claim you did so.
Removing the drive should not compromise the forensic aspect, as long as you document the procedure. When did you get the computer in question and from whom. Document the computer so its identifiable without question. Document the make, model and serial number of the drive you are duplicating. Document the duplication process, what equipment and software you used.
You might want to spend some time reading this site, which includes links to some write blockers which are less expensive than forensic duplicators. http://www.forensicswiki.org/wiki/Main_Page