http://www.laurels.com/stopwatch.htm
are just a couple timers with RS-232 options.
An alternative would be to activate a switch or relay when the device is on, connect the relay (debounce or use solid state) to a digital input of a DAQ card, and write a LV program to time how long inputs have been activated. You may want to log data to disk every so often in case of PC crash or loss of power.
Unclear as to your remote readout needs.
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