Two External Monitors on a 2013 Slim iMac

From Apple's "Thunderbolt ports and displays: Frequently asked questions (FAQ)" web page:
Note: Systems with more than one Thunderbolt port, like an iMac, can have more than one Mini DisplayPort monitor or monitor connected with a Mini DisplayPort adapter connected as each Thunderbolt port can support one Mini DisplayPort display.

This information suggests that what you (OP) are trying to do should work.

Also, for the OP, I think your Thunderbolt to DVI and Thunderbolt to VGA cables are actually Mini DisplayPort to ... cables. I'm not aware of any actual Thunderbolt (TB) to DIV/VGA/HDMI cables. The available Mini DisplayPort adapters cannot drive a display directly from an Apple Thunderbolt Display (ATD), as they (the adapters) require a Mini Displayport (MDP) input signal, rather than a Thunderbolt input signal (they are not the same!), and the ATD can't send a MDP signal out it's second port, it can only send out TB. Eh, perhaps that's all a bit off-topic, sorry.

Um, did you try the PRAM reset?
 
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