I had what sounds like the same exact issue as you, so hopefully the solution is the same. No amount of cleaning the rollers or tinkering would fix the problem. In fact, it seemed like the feeder rollers weren't spinning at all.
I dug up the service manual online and proceeded to take everything apart until I could get to the gearing and have a look for anything out of place.
There is a small plastic lever that is used to lift/lower a gear in order to start and stop the feeder rollers. This lever can come out of position such that it can no longer wedge beneath the gear, and instead pushes against the side of the gear. Thus, the feeder rollers will no longer work.
Fortunately, the problem exists in a place that requires no disassembly.
1. Remove the paper tray.
2. Facing the printer from the front: Immediately to the left of the paper tray slot, there is a small hole (Circled in RED) with a white piece of plastic visible through it (Squared in BLUE). This white piece of plastic is the lever we need to put back into position. If it looks like in my photo, it's where it should be. If you see less of the white plastic, it is out of position.
Before step 3: Notice the curved slot (Underlined in YELLOW) directly beneath the hole where the white plastic lever lives. There is a very small clip/hook on the lever which is supposed to rest in this slot, keeping the lever from dislodging and causing the very issue we are having. If you look into the slot, you should be able to see the clip. When I did this fix, this clip broke because I was impatient. You will need to gently flex the clip up (toward the top of the printer) while following step 3, so that it seats correctly in the curved slot.
3. With some small pliers/needle nose, grab the white plastic piece as seen in the image and gently but firmly pull it toward the right side of the printer (BLUE arrow). It should slide into the correct position, and the small clip should latch into the slot, hopefully stopping this from ever happening again. If you fail to flex the clip up, it will press against the inside of the printer's casing and snap off.
-- If the clip breaks like mine, it's not the end of the world. You'll just be more likely to need to do this simple process again in the future.
4. Slide the paper tray back in and give it a whirl. Hopefully it works for you.