Try a new belt:
I have a PX-3 and have done quite a bit of work on the tonearm transport mechanism as it occasionally would "stick" on a spot just prior to where it would drop to the record surface. In my case, years of not operating it caused enough dirt (dust) to collect on the rails and small plastic transport wheels to cause the sticking. Once I opened it up, did a thorough cleaning of the entire mechanism (which will require some patience, need to remove the entire transport mechanism, then the transport belt to get the tonearm off the rail to access the rail and transport wheels). Take care NOT to use any type of lubricant, just make sure the rail and wheels are super clean by wiping with a soft, clean cloth and a bit of distilled water is what I used. While in there, make sure your tension springs on the transport mechanism are keeping that wide, flat belt taught as well. If not, you can shorten the springs by bending the small hooks on each end in a bit closer to the coil. Mine didn't require that, but I have read where several others have needed to do that. From your description, if the arm does not move at all when you press the "30" button, and needs a push towards the left, it may well be that your automatic sensor, called the "right limit switch," is sticking so it would be wise to check this switch while you are at it. Looking at the assembley from the rear, you will notice that when the tonearm is "parked" that the switch is depressed. When you move the arm towards the right, looking from the rear, you will hear a bit of a click indicating it has released. My bet would be that the tonearm unit is sticking right at this point and a bit of cleaning should free it up. Otherwise, check and clean all the push buttons although I doubt, from your descripton, that it would be any of those.
Good luck, and if you need a service manual, I have one for the PX-3 that should give you some pretty good ideas on what to do with the PX-2 as there are many similarities I understand. Just get me your email and I'll send you the PDF.