The computer will run on any waveform that reaches a high enough voltage, but over time modified sine wave inverters will usually destroy the capacitors in the computer power supply. Sometimes this can take months, sometimes a few weeks, and in some cases even a few days. People have run computers from modified sine wave inverters for years, but it all depends on how well the power supply was made, how good the components are that they built the supply with, etc.
In my case I have seen my desktop power supplies go bad within one year. I have also lost DirectTV receivers within one year. If the power supply is made as a DC converter with high quality components and is engineered well then they can last for years with no problems on modified sine.
Running straight filtered DC from panels etc directly into the device (if it is a dc-dc converter) would be easier on it than modified sine wave.