I've previously mentioned the difficulties I've had getting the HP DeskJet 2500CM that I recently acquired operating properly.
The photo below, not my photo or my printer, gives some idea of what it looks like, by the way, but not how big this thing is. That's not letter paper in the output tray, it's 11x17. The printer is about three feet wide by more than two feet deep front to back, weighs about 120lb, and will print -- full bleed -- on paper as large as 13"x19".

Today, having obtained a service manual on CD for it, I tore the entire printer down as far as (well, actually somewhat further than) documented in the service manual.
(I'm not very impressed with the service and support manual. A reasonably competent monkey that was good with common hand tools could probably learn all the mechanical service procedures in the manual. All the service procedures are based around swapping out entire assemblies; there's no repair for anything, no replacement of individual mechanical parts¹, and even most consumable elements aren't replaced. Ink bin fills up? Just swap out the entire "service station".)
This process of disassembly led to the extraction of about seven errant foam packing peanuts from various nooks and crannies in the mechanism, several of which were doubtless interfering with things. It also led to the discovery that the little domino-shaped paper size indicator insert from tray 2 was not missing, as we had thought; it had been shaken loose during shipping and ended up in the paper feed mechanism, where it was completely blocking the feeding of paper from trays 1 and 2. Further, I discovered a truly astounding accumulation of dried ink (waste from cleaning cycles, I assume) in the ink bin of the "service station". The cleaning transfer wheel was black instead of grey (I didn't discover it was grey until I took it off and washed it), and the ink bin, about the size of a small deck of cards, was half full of black goo with the consistency of half-dried putty. Basically anything that was dirty that I could get at to clean, got cleaned.
Anyway, after dealing with all of this stuff, and making a simple but very effective field-expedient repair for the annoyingly hit-or-miss power switch, I put it all back together, found a copy of the REAL JetAdmin tool (as distinct from that steaming pile of fetid dingos' kidneys that HP fobs off as "Web JetAdmin", and which is in my experience completely and utterly useless), set up direct-to-the-printer printer devices on the Windows box, and started testing. It's now working much better, and appears to be feeding properly from all three trays and the manual feed (but if you're printing from manual feed, better have your paper loaded in advance, it's pretty aggressive about grabbing it).
Our printer lacks the lower tray extension cover shown in the photo. It's not required, but is recommended when tray 3 is extended to hold 11x17 or larger paper. I'd like to pick one up sometime, if I can get my hands on one.
[1] Well, actually, there's three exceptions to this, it appears -- the encoder strip, the paper advance wheel, and oddly enough, the power button. Not the switch, the button. Three individual logic boards and the LCD display can also be separately replaced.