video mode unuseable upon waking from sleep mode

I've been using this Windows 7 Home system for some years. At first it used the CRT monitor I had for much longer than this system, then a used LCD monitor, now for the last six or eight months a larger used, but seemingly in excellent condition, Dell E228WFP.

My habit has been, for much longer than I've had the Win7 system, to manually put the system in sleep mode during the day when I expect to be away for any extended time. I turn it off if I will definitely be away for hours and turn it off over night.

The problem did not exist until this Dell monitor. I don't recall how soon after getting the monitor it started, probably not very long.

The system always come up working properly when first turned on but sometimes, when I awaken the system, the video is at a much lower resolution. Looking at the Windows Screen resolution, it says generic PNP monitor rather than the Dell. This is an annoyance but easy enough to fix, just click on Detect, and it switches back to the Dell at the higher resolution, the recommended 1680 X 1050, which is enough to suit me.

Starting perhaps six or eight weeks ago it sometimes instead woke up with a message
1: auto detect (analog input)
Cannot display this video mode
optimum resolution 1680 x 1050 60Hz

Sometime the first line instead says
2: Analog Input

The only way to get any video is to restart the system, which always came up correct from boot or reboot, just not from reawaken. If nothing was open when I put it to sleep, I can use the keyboard sequence to Restart. If various programs are open when I put it to sleep, which is often, only a hardware restart works because I can't see the message that ask what to do about the open applications.

This is much more annoying and inconvenient than the original low resolution opening, and possibly a totally different problem. Now, quite recently, it has started sometime coming up when first turned on with the message, and no video. Yesterday I had to restart the system twice to get things working. This doesn't seem like a good trend.

I don't know where to look. Windows obviously can tell what monitor and what resolution but doesn't always do so -- or something is being presented that is a strange video mode that can't be handled.
Is it a faulty monitor (which never misbehaves once it is running properly)?
Is it some Windows setting?
Is there any way to find out what "this video mode" means?
Where to start?

It occurred to me to check Device Manger, to see if I have any control there. I have been doing everything by right clicking on the desktop and selection Screen resolution. Under Monitors there is only
Generic Non-PnP Monitor
There is no option to change anything.

Perhaps I just didn't read carefully and this is also what it says under Screen resolution when it comes awake at the much lower resolution. I can't produce the condition on demand so I can't check right now. When the Dell is shown there is no other option under Display:.