3805 Remote
I'm chiming in here to say I had a similar prob with my 3805 remote. Dim, virtually unreadable display.
If you press the "select" button with the "channel +" button, you should be able to increase the visibility of the display. Try that. It didn't help my problem, but it's worth trying.
If you press the "on" and "off" buttons simultaneously, you should get a screen of numbers. Check the owner's manual for the exact combo of numbers, but if my memory serves, I pressed "4" to set the display time (i.e., the lag time before the display light turns off). There are several options (2 seconds, 5 seconds, 10 seconds, 20 seconds) and, depending on which number you push, you set the display time. Try that. It didn't help my problem, but it's worth trying.
If you take all the batteries out and let the display sit for a minute, then put in all new batteries, I think you get a display reset (factory-set dimness and display time). Try that. That's what finally worked for me.
If the above suggestions don't work, I'm out of advice. You might try calling Denon at that point, or sending the remote back to them for a new one ...
Good luck!
Zarg