It helps to picture the setup but frankly I'm stumped.
You've done all the tests, swapped the monitor and tried the Lenovo monitor on another system, and another monitor on this system. That is what i would have suggested. They all work, so where is the problem? I'm not sure.
Is this Lenovo desktop the same as this one? http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=3523912&CatId=
If so, I see it has a Power Dial on the front which allows certain features to be 'ramped up'. I wonder if that dial has been used somehow and the system is now unstable?
I can't say more than that because I have never used one.
Tell us again when the monitor starts flashing.
There is a possibility and if you don't know here are the two alternatives when we "switch on"
1] Power on and the maker's Logo image appears until Windows begins to load. Whilst the logo is displayed, you can not see any other messages.
2] Power on and there is no logo. Instead the system's BIOS, (Basic Input Output System), performs its POST checks, (Power On Self Test), and displays messages on the screen. This is the BIOS checking all the hardware in the system, the motherboard, USB ports, video card, hard drives, and so on. These messages can cycle through very quickly so it might look like the display is flashing, but all these screens are black with some white text on it.
In each case Windows does not begin to load straight away because the BIOS has to complete its checks and confirm the hardware is all working. If it wasn't the BIOS would not pass control over to Windows and Windows would not begin to load.
When Windows does begin to load you see a small logo, and perhaps a progress bar. After a while you should see a blue screen called the Welcome Screen, and then your Windows Log in Accounts options should be displayed. You then choose your account, type in the password, press Enter, then the Windows Desktop will display.
So my previous question was, where does the monitor begin flashing? But also, does your Lenovo perform like item 1 above, or item 2 above?
Mark