There's no need to mention it was unpaid, unless it was infrequent enough that you think the company would deny you worked there at all. If the other part-time job was at the same company, I think your CV would look like this (newest role first - so, reverse chronological order):

Other Job, CORP: Other job's responsibilities, and additional sysadmin work (specific technologies or routine tasks)

Sysadmin + Other Job, CORP: Job responsibilities