Pi4, 4G, latest Buster, installed via the latest PINN, dual monitor system.
But by no means limited to the above set of circumstances - seems to happen always on this particular hardware config with Buster.
The problem is that when ever the machine is cold booted (from power on), the main monitor ends up black. There is a X desktop visible on the second monitor, but no lxpanel or icons, so you can't do anything (except see below). Rebooting fixes the problem - system comes up correctly on the reboot. But it always fails on the cold boot.
Note: You can get a shell going on the second monitor by doing the following steps:
1) Ctrl/Alt/F2
2) login on tty2
3) Execute: DISPLAY=:0.0 lxterminal
4) Alt/F7 (or F1 - see below) to get back to the desktop - where the shell will now be running.
Also note: It seems that somewhere along the way, they may have made the switch to running the GUI on tty1 instead of on tty7. As noted by me elsewhere, the latest cutting-edge versions of Debian Linux now run the GUI on tty1 instead of tty7. This is done in the name of "security". There are certain circumstances in which Raspbian is now doing this (I have not investigated thoroughly enough to be able to authoritatively state what those conditions are, but I have definitely seen it in today's testing).

