Parkonsons disease is usually responsive to sinemet, although a trial of up to 1000mg per day may be necessary to confirm this.
The tremor of parkinsons is a rest tremor, but can appear somewhat postural also, but should disappear in the early stages with movement. Make sure the arm is completely rested and limp before saying that he does not have a resting tremor. It can be commonly confused with a number of other causes of tremor such as familial benign essential tremor - if there is a family history of tremor or responsiveness to alcohol this is more likely. A pinched nerve in the neck (neck pain may be a clue) could make a physiological (ie within normal limits) tremor worse or appear. Tremor can also occir from medications (have these checked out) or brainstem problems (ie old stroke) - in this case it is important to get an MRI of the brain to exclude these. The best person to delineate the diagnosis (I cannot do this over the internet) is a neurologist with specialized training in movement disorders - this is your best bet, they are available at most major medical centers, and they are specifically trained in identifying all the mimics of parkinsons disease.
Good luck