Potato battery not powering clock
a simple 1.5 volt led clock


Well, there's your problem. You don't want an LED clock. You want an LCD clock. LEDs take (relatively speaking) a lot of current, and a potato battery simply won't supply it. As a check on this, go back to your potato/clock combo, and measure the voltage with the clock connected. Notice something? Your voltage is almost zero with a load on the potato.

I suggest you go on Youtube and search for potato clock. This will give you videos which provide a source for an appropriate clock.

If, as you say, you cannot buy such a clock, you are probably out of luck. About the only alternative is to find a clock, or perhaps a watch, which runs on a single alkaline battery. You can figure out which battery connections to connect to which electrodes you have and go from there. 

But LED and mechanical clocks simply will not work with a single potato.