The answer isn't out there, alas, but the topic has been raised some times since 2.0, indeed.
I too have a Windows computer, not so old, but in the middle range of performance of the time. This is an HP computer: they are great for their reasonable price, except for the graphics card, often cheap and low performance (often an integrated Intel chip... Mmm, I have an AMP CPU, so it is an ATI Radeon HD 5450, probably not the fastest of the block, even at the time).

Indeed, since 2.0, whenever I attempt to do a 3D sketch (or, more often, to run one from the forum), I often have to wait for around 30 seconds before getting anything on the sketch area! Looks like OpenGL is slow to start here. In general, the second run is much faster, fortunately.
One potential fix is to upgrade the drivers, but I always applied the latest proposed by the auto-update.
Except upgrading to a more powerful graphics card, I don't know if there is a general fix (perhaps play with the settings of the card).

You can use 1.5.1, still available to download, with its old P3D mode (simulated 3D) or less advanced OpenGL mode.
I think there is also a library recreating the P2D / P3D modes for 2.0.

PhiLoh,
 Thanks for the reply and for taking the time to send it.  These are cluster machines at Carnegie Mellon University and they probably do not have anything beyond the standard graphics capabilities for such machines.  So, I will report the problem to the Sys folks and probably  just "live" with it.  Many if not most of my students have their own machines to use so things will work out or they will have to stay in 2-D...

 Also, I find that P3D and P2D are still working in the current Processing 2.0.1 -- I thought they were not going to work going forward.  Any thoughts on relying on those if they are working.

 Regardless, thank you very much for the information.

Jim