Cinnamon is more demanding of your graphics card driver than GNOME 2, which you probably used on Linux Mint 10 and 11. As you already mentioned that you ran into the same kernel panics with Linux Mint 11, which was still on GNOME 2, probably that's not going to make a difference.
You mention you were able to boot Linux Mint 13 from the USB with compatibility mode + nomodeset. Now that you have it installed, just nomodeset doesn't work. So I suggest you add the boot parameters which compatibility mode included. That would be the following set, so try adding those and don't trip over the spelling of the first two
Also, remove "quiet splash" from the current boot parameters list.
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noapic noapci nosplash irqpoll xforcevesa nomodeset b43.blacklist=yes
But xforcevesa is for AMD graphics cards mostly, and b43.blacklist=yes is for Broadcom network interfaces. So you can instead use the following set. You might want to play around with this a bit, and see what the minimum combination of boot parameters is that you need to boot to the desktop. The less boot parameters you need, the better experience you will have!
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noapic noapci nosplash irqpoll nomodeset
If this allows you to boot, hurray. But it will probably not be a very good experience. You will probably want to open Additional Drivers from the menu, and see if there are additional drivers to install for your graphics cards and for your network interfaces. The network interfaces may be problematic on Linux, so I hope you can get either one to work before going to Additional Drivers. As for having two graphics cards, I don't know what the right steps for that are. Perhaps it will work fine if that is supported by Nvidia's driver on Linux.
With the proper drivers installed, you should hopefully not need the boot parameters any longer.