Bernie - As far a the clock running fast, I supsect one of two things. The frequency of the inverter is way off or the clock is picking up "steps" in the modified sine wave that comes out of the inverter. I suspect the latter since you are not finding problems with other electronics...the TV. The clock you have probably does not convert the power to DC and keeps time, like most household clocks, by expecting the frequency to be 60 Hz...a very accurate method usually, since it is controlled by the electric companies. However, if the inverter has a modified sine wave output (instead of a pure sine wave), and most do, the clock is probable sensing the steps in the sine wave and triggering off some of them to increment each second prematurely. I wouldn't worry about the computer because and internal power supply will convert power to DC and probably have enough filtering to provide clean power to the computer components. Computers are pretty forgiving about the input power because of the clean-up work done by the internal power supplies.
'01 Alpine 36 FDDS