I suspect the answer to this is "no", but here goes:
I have a monitor with inputs for DVI and VGA. I want to be able to share this display with two computers (one at a time, of course) that both have VGA only. I also have a DVI->VGA dongle that came with a video card that's in a different computer.
Can I connect this dongle directly to the DVI port on the monitor so that I can connect both VGA computers? I'd rather not resort to a kvm.
No, you'll need to use the KVM option or buy a couple of VGA extension cables and manually switch between the two (bring the two monitor ends of the extensions and the PC end of the monitor's table up to you test and hold them there with something like http://lifehacker.com/5499838/binder-clips-as-cable-catchers-redux%5D and just plug the monitor one into the right extension when you need to). You might find a cheap 2-machine KVM with the required cables doesn't cost much more than a couple of plain VGA extension cables though.
A DVI->VGA "converter" doesn't actually convert any signals at all. Most DVI ports on graphics cards also carry the analog RGB signals needed by a VGA monitor along side the digital signal lines (see http://en.wikipedia.org/wiki/Digital_Visual_Interface for relevant pinout diagrams) and all the adaptor does is connect these pins to the right pins of the VGA port. So unless your monitor can accept the reverse (analog signals through its DVI input), which I doubt many (if any) do, this does not work the other way around.
Nope. The DVI-->VGA dongle is actually "DVI-I" to VGA. The "I" representing that the DVI port has the analog signals needed to convert to analog VGA.
Since the Monitor doesn't produce a signal (analog or otherwise) they only have DVI-D ports on them ("D" being 'digital-only'), so you won't even be able to plug the dongle into the port (the spade is the wrong size, and there will be 4 extra pins on the dongle (these are the analog signal pins).
