Hmm, just now noticed you've replied (I gave up after waiting for two weeks

)...
These are the only ASUS 6970 cards I could find:
http://uk.asus.com/Graphics_Cards/AMD_Series/EAH69702DI2S2GD5
http://uk.asus.com/Graphics_Cards/AMD_Series/EAH6970_DCII2DI4S2GD5
Is either one of them yours? I'm a little worried, because you said your GPU only had HDMI and DVI, but these also have DisplayPorts. Hmm, could you also check the GPU manual and see if there's ANY mention of DVI-I ? That would really clear things up. The rest of the post is made on the assumption that your GPU is indeed one of those.
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Well, as it so seems (if above is right), your GPU has one DVI-I port, and one DVI-D port. DVI-D is only capable of digital signals so that won't work, but the DVI-I should be OK for VGA (for analog signal).
First things first, just to make sure:
Can you get the native resolution and refresh rate 1600x1200@60Hz (or anything at all, for that matter) with the "DVI-VGA-cable + VGA-DVI adapter" combination? DVI-DVI cable is probably with pins for digital signals, so we're not interested in that. Actually, you can put the DVI-DVI cable aside for now. Only use the "DVI-VGA + VGA-DVI". Try both ports on the GPU (actually, there should be a mark for "VGA" on the other port, try that first) and both ports on the monitor, too. You might have to restart in between the changes. It's at least recommendable.
And just to clear something: 75Hz is not a LOW refresh rate for LCD technology. 60Hz is the standard refresh rate, and it's what basically every LCD monitor uses by default. The highest refresh rates for consumer monitors are 144Hz at the moment.
Regarding MAME (arcade games, right?) and lower refresh rates:
I don't have that much knowledge about arcade machines, but I'd reckon they use either 50 or 60 Hz refresh rate? Neither should be a problem for LCDs, I think. And even if they use 30 Hz, that's exactly at half point of 60Hz, so you would be better off using the 60Hz (there shouldn't be any disadvantage from running it at 60Hz, it just shows the same frame twice).
Well, that's a secondary issue, in any case. Let's first try to figure out whether the analog signal is possible or not...
Oh and btw, the numbers with MHz and kHz in the earlier posts are different kind of clock rates, they're not the refresh rate of the monitor itself. Like I said, they're more technical figures, relating to the electronics inside, don't worry about them for now.