Hmmm. Sounds like you might be getting a bit of a shock off of it. Be careful. Generally, on these touch lamps, the only thing standing between you and the AC mains voltage is a small pF capacitor. Not a repair I would recommend for a beginner. So if you are one, follow Sceadwian's advice.
How to test a triac.
The circuit above, using 12Vdc, is a good simple test circuit. The explanation is a little off, but the idea is correct:
With S2 ON, momentarily pushing S1 should light the lamp and it should stay lit until S2 is turned OFF and the ON again. Not a 100% bullet proof test, but good enough for practical purposes.