The HP EliteDesk 800 G4 TWR supports 8th Gen only — no 7th, no 9th

The G4 TWR supports 8th Gen Coffee Lake processors exclusively — i3-8100, i5-8400 through 8600, i7-8700 and 8700K, plus Xeon E-2100 series parts. You can’t fit 7th Gen Kaby Lake (despite the same LGA 1151 socket) nor 9th Gen chips. Intel changed the pinout with Coffee Lake even though the socket looks identical, and HP’s Q370 chipset implementation enforces that line strictly.