1) Remove the faucet aerator screen - it could be clogged or rusted shut
2) Remove the valve(s) and inspect the rubber seals and springs - they may be clogged, hard and stuck, broken completely.
3) Since it was bought used, you could also have non-standard shut off valves in the lines or some other bizarre problem.
Lou and Laura with Bella - German Short Hair Pointer
2008 GMC Sierra 2500HD Crewcab SB Allison Duramax
2010 Flagstaff 8526RLWS - Superglide 3300
HAM CALLSIGN - KC3FFW