IMac – Using an iMac 27 inch (2009) as a monitor for a mac mini with Lion

As it turns out, it was the Mini DisplayPort-to-HDMI cable. I connected the secondary monitor with a Mini DisplayPort-to-HDMI Adapter and everything works fine.

To the best of my knowledge, the cable is fine, although, apparently, it is an unlicensed HDMI cable, and manufacturers can no longer sell them. Has Apple dropped support for these? Not sure. At least everything works again.

The mini DisplayPort to DVI adapter will work great, so your 27" monitor is in.

The VGA monitor is problematic. HDMI and DVI share almost identical digital video signals, so any HDMI to DVI adapter (like the included one) has few (if any) conversion chips in it and the output DVI port will be DVI-D (digital only). DVI to VGA adapters also don't have conversion chips because they use DVI-I or DVI-A ports (A is analog only and I id both analog and digital): they take the DVI analog signal and move it straight to the VGA port. Unfortunately, that means that you cannot go from HDMI to VGA via DVI. You'll need a more expensive converter like this or this.

tl;dr: You can't go from HDMI to VGA without a converter; see the links for examples. For the dual-link DVI you need, the adapter you mentioned that will use the Thunderbolt port will work excellently.