How does an inverter affect the computer?
I assume the question is not about power efficiency differences with a system on sine-wave power versus not-quite-sine-wave power.

Recent laptop power bricks and desktop power supplies are switched mode power supplies (SMPS). An SMPS typically rectifies the power line voltage, then uses a high frequency oscillator to "chop" this DC, a small transformer to step this switching voltage down as well as isolate it from the power line, and finally regulates the output voltage to the required levels using an integrated sense mechanism feeding back to the high frequency oscillator. 

An SMPS is not particularly sensitive to power line waveform, as the rectifier stage turns it all into a ripply form of DC anyway. Yes, the high voltage section immediately after power line rectification would see a difference in voltage due to waveform change, but that doesn't matter very much: Many "universal" SMPS designs are rated for 90-250 Volts 50/60 Hz operation anyway.

If the power line supply is a square wave, the higher harmonics might stress some components in the high voltage portion of the SMPS beyond their ideal design parameters. Also, there is a tiny possibility of higher-harmonic noise sneaking onto the output rails.

However, typical inverters, even the poor quality ones we have analyzed for some projects, tend to deliver at least a somewhat smoothed trapezoidal waveform rather than a square wave. Adverse impact on the SMPS is negligible in such cases.

If the SMPS is reasonably well-designed, the actual computing hardware (laptop, or desktop motherboard) will not face any problems due to non-sine power line waveforms.