I was just playing with my friend in a dungeon until I couldn't click anything. Seeing as I was still able to type into chat, it wasn't my keyboard (laptop keyboard with mouse). I couldn't click anything and spell cards weren't enlarging when I put the cursor over it, but it was still lit up (when I put the cursor over it) like normal. This wasn't the first time this has happened though, and out of all the people I've played with, this has only happened to me. I also have a touchscreen and even that wasn't working.
Is this because of my mouse or is it a bug in the game?
This does sound isolated to your computer unfortunately. Are all your drivers up to date? You may want to contact support and provide them with a DxDiag file from your computer to see if they can help identify any issues.
I too have had this issue, however it seems to be when my internet connection is spotty. Basically, anytime there are connectivity issues I've experienced this or alternatively just a randomly disappearing cursor. (cards become larger and highlight, just no cursor, though this is slightly rarer than the way described by Valdus for me anyway.)
I've never had this with a singe window open, but it's common (for me and friends) when dual or triple boxing. The fix then is to minimize then enlarge the window, or to alt-tab switch windows. Usually when the focus returns to the window, the visible cursor does too.
