trabe3
Yes, it has been a problem for some users.  It is due to an incompatibility with your motherboard BIOS.  That is main issue with lots of the prebuilt systems from HP, Dell, Acer, etc.  Sometimes they make an updated BIOS, but most times not, like you are experiencing.
 
As far as motherboard, I assume you are going to reuse your CPU, so you will need to keep the same 1155 socket obviously.  Everyone has their favorite brands, you probably can't go wrong with most of them.  I personally don't care for Gigabyte, but that is just my preference and I remember some people having BIOS issues with 700 series cards as well with that brand.  MSI, Asus, AsRock, all are decent.
 
One other component to check would be your power supply.  Make sure it is capable and sized for the new system.  Most OEM power supplies are lower quality and may not be up to the task of a higher end card such as your 780.  I would recommend looking into replacing with a quality 600W minimum one, unless you are planning on more upgrades such as adding another video card at some point, then probably bump up to 750-800W minimum.
 
Hope this helps, post back if you need any more assistance.  Good luck!

trabe3
I think that motherboard will work, but don't know for sure.  You might want to consider ditching the HP case and buy a larger case that would be able to use a more standard ATX board.  I think you would be happier in the long run.  But if you decide to go the route of swapping the motherboard, let us know how it goes.  Good luck!