This sounds obvious to ask but neither of these monitors have DVI? I don't think the Switt does correct, but neither does the Gateway? I find that hard to believe for any computer monitor made in the last 3-5 years. Usually if there is more then VGA (and you are saying there is component in) there is usually a DVI port.

A simple HDMI-DVI cable is all that is needed in this case. I use that cable with a mini-HDMI male to HDMI female cable on my 5D and all is well.

The switt has a vga and the Gateway has dvi. I have a hdmi- dvi adapter, whuch I tried on the gateway, but got no signal.
I assumed it wouldn't work, so I ordered the hd fury. Hope it works.
Bruce Yarock

Strange because I have two hdmi-dvi cables that both work and onw hdmi-dvi adapter that works as well on my gateway FPD2185W. I even love the fact that on this monitor if you set it to zoom when you start recording and the 5D goes in to 480 mode, the monitor still has this huge image (although obviously pixelated).

Up date-

I get the 7D to play through the gtrway with an adpter pluf that goes from hdmi to dvi. It lloks good but the image is not fill screen ( no idea).
I had orederd the Fury HD 11, and ried it on my Sony monitor, and unfortunately, it won't work without the piwer supply. When powered it looks great.
this is a pain in the ass because I wnted to be able to also monitor the 7d oit doors through my Switt. But if the HD Fury needs power, that won't work.

When I have tome, I'll try the HD furey with my Gteway and Switt.
Bruce yarock

Bruce check to see if you have a zoom option on your gateway. If you choose that over 1:1 in video scaling, the image will fill the screen. Just note that it's still only 480p so it's going to be really low-res, but for me, that's fine since the type of shooting I do I can focus adequate on the low-res.

barry,
I got Fuyru HD11 from monoprice, and tried in both my Gateway and a sony high def crt television. Looks great on both, but one big problem...It won't work without the power supply! This is ok indoors but doesn't help me on location, where I wanted to use it with the Switt monitor.
I'm using a 6' mini to regular hdmi cable from radio shack, connected to the Fury HD ii. You said that yours works with 7d without the power suppley. Any idera why mine wouldn't?
Bruce Yarock
Yarock Video and Photo

Update - my 7D does power the HD Fury II, but -- not enough. It works for a little while, and then it looks like the intensity of the signal drops about 10-15%. I've taken to using the HD Fury's power supply even with the 7D. Even though the 7D does supply HDMI power, I don't think it's enough to make the system work properly.