Sorry for the delay, I "ran" the following tests on one of the RPis as the symptoms are the same for both:
1. Monitor only: Screen just sitting on login, after a minute or so only PWR led remains on. Plugging in input like mouse/keyboard doesn't do anything.
2. Monitor+ethernet cable: Screen sitting on login, showing lan ip .XXX after less than a minute, only PWR led is on. The device is actually not on the network (ssh / ping attempts come up "unreachable")
Note that the pi still got to login screen after this screenshot.
3. Monitor+usb wifi+usb keyboard/mouse: errors visible at boot, pi gets to login screen but then only PWR led stays on and the device is unresponsive
4. Monitor+ethernet cable+usb keyboard: got to login no errors, logged in using keyboard, after ~15 seconds of "idling" all leds went off except for PWR and the pi didn't respond to keyboard input. After another 5-10 seconds the leds momentarily started blinking again for about three seconds during which I could type again. Then back to PWR-only non-responsiveness forever.
All the components (wifi card, keyboard/mouse combo, keyboard) I used in this test work fine with the "working" RPi units I have.