Hi Russ,
One of the "incentives" to moving their product lines to command control (with Lionel to TMCC, and with MTH, to DCS, e.g. PS2) was that it would uncomplicate the situation you're experiencing. PS1 is very complicated, mostly because you only have three buttons, direction and whistle/horn (on traditional transformers) and bell (on newer transformers), and a throttle, to use in configurating and operating a locomotive's advanced features. Hence the need for sequences of button pushes, and corresponding 'clinks' and 'clanks'.
If the previous owner of your piece didn't configure too many features using this method then it should start right up and go using the following steps:
1.) Setup -- With the unit on the track apply track voltage, using the throttle, to a high setting, say 95% of full throttle.
2.) Charge -- Wait for the internal rechargeable battery to charge. If the unit has been sitting for months this may take a couple hours. If it's only been a few days this will be quick. If it's been many years you probably need to install a new battery (the so-called "green" battery from MTH) before following Step 1 above. In a pinch you can use a common 9v alkaline battery, but only temporarily and for only a short period, to see if the unit is functional.
3.) Ready -- Lower the throttle to around 8 VAC. How you determine that you're actually at 8 VAC is up to you. I would recommend using a Volt Ohmmeter (VOM). With classic transformers like a TW or ZW the reading you take will be quite accurate, with modern ones it should be close enough. But you may have success by simply moving the throttle to half (50%), or a quarter of full (25%). Why 8 VAC? It seems to work best with all my PS1 equipment and the suggestion comes from reliable sources. When you get to 8 VAC you should hear a 'woosh' followed by a 'thunk' that kind of sounds like the transmission on an old car dropping into drive when you shift it to 'D'.
4.) Run -- You're now in the first position of the traditional sequence Neutral - Forward - Neutral - Reverse. Cycle the throttle down to zero and back, or push the direction button, and it should begin rolling down the track just like a normal traditional locomotive. If for some reason the previous owner had locked it into one direction, or another, F or R, it won't cycle through the sequence N - F - R - N etc. but will only go one direction. Worse, if it was locked into 'N' it won't go at all without being reset using those button pushes, and clinks and clanks.
At this point as long as you don't shut the throttle off for more that about 30 seconds you'll continue to be in this mode for your entire operating session. If you go to zero volts for more than that time you need to go back to Step 1 above.
Is this ridiculously complex just to get the train to move? Maybe. Does it work? Most of the time, but not always. I can get mine to roll, using this set of steps 9 times out of 10, on average. Not bad, but not perfect either.
Mike