I'd try a range of things, and I'm sure others will have more to add, but I would:
Check the camera physically to make sure the screen works, buttons, EVF, etc
I'd update the firmware straight away to the latest
Put on several lenses and test that they're recognised correctly and the AF and OIS are working
After putting in a new battery and formatting a memory card in it, I'd pick the best quality normal mode (24/25/30p) and do a long recording on it of something that has a lot of movement in it (a great test is putting three still images on a timeline each at 1 frame and then loop the video).. if it records without issue for 20+ minutes without anything odd happening that's good, but if you have time I'd test until the card fills up or the battery dies
I'd also do the same but on the highest frame rate mode
Check the files are playable in the camera and work on the computer
If it passes all of the above then it's unlikely that it has some lingering issue that isn't also present on new copies as well.