Darkening of the cell suspension during sonication can result from overheating if the sonication goes on too long without enough time for cooling. The overheated protein is likely to become denatured and precipitate.

I am unsure if you are purifying your protein from the inclusion body. In case you are, I suppose sonication may not have occurred properly if the pellet you got after sonication is brown. In my experience, successful sonication usually brings out a whiter shade of inclusion body pellet. The brown color may therefore account for the presence of some cellular debris. Perhaps increasing the amplitude or total time or using a different probe during sonication may help. I hope you are keeping samples on ice while sonicating and keeping the single cycle such that the time off sonication is enough not to heat the samples. Say 10 seconds ON and 50 seconds OFF. Since you mentioned that you could not purify the protein, I suppose the expression was still there, but there were other contaminants along with your protein in SDS-PAGE?