2011 MacBook Pro white screen

There were a couple of different models in 2011. The early 2011 came with Snow Leopard on a disk - which is what you would need in order to get to the old version of internet recovery and disk utility. They are unable to use the recovery options of newer models/OS versions.

Sounds like some sort of hardware issue with the laptop. If you have a 15" or 17" model, then it is likely the GPU has failed which is common with those models. There is a slim chance that a failing hard drive could prevent the Mac from booting to any media...removing the internal drive and trying to boot into Internet Recovery Mode or bootable macOS USB installer should now work if the internal drive was the source of the problem.