A 20 Billion market cap is quite large, even with so much cash on hand, it would still likely take several PE firms to team up and take it private. It would amount to one of the largest PE deals in history.
I don't think taking the company private would directly solve any of Dell's problems, but it might help them shore up some internal inefficiencies.
Historically, Dell has been successful through its efficient supply chain and ability to reap high margins from low cost/high volume PC manufacturing.
In the long run, I don't think staying this path will be sustainable for Dell. Asian manufacturers are rapidly taking stage as the go to hub for cheap PCs and manufacturing.
Instead of trying to leverage rapidly diminishing returns on optimizing efficiencies in PC manufacturing and supply chain, Dell should focus on the (painful,expensive) transition towards shifting its focus towards enterprise tech and enterprise consulting.
Opening a venture arm is a step in the right direction towards gaining a foothold on some new tech verticals.