Trying to breathe new life into old machines is going to be painful. Refurbishing the machines (strip, clean and rebuild) is a good start. Also test the HDD smart and replace CPU fans if possible. -- Finding parts may be a challenge.
Assuming the school is running XP, maybe do a fresh install, install SP3 and the latest RDP client. Investigate write filtering (goggle fbwf) so that the main OS is locked, but the profiles directory / %temp% is not.
Using the new features of terminal ervices, you can publish an app instead of an entire desktop, so that may be a consideration for you.