Brand new camera and brand new SD card...after charging the battery tried inserting SD card and got the "This memory card cannot be used..." error message. The car is new and never formatted. I tried 2 other SD cards and got the same message. Defective camera?
Could be a defective camera. Are the SD cards the proper type specified in your camera manual? (Regular SD, SDHC, SDXC)? Also make sure the speed class of the card(s) are correct for the camera (Class 4, Class 10, etc.)
Thinking about it some more, I don't think it is a defective camera. Probably incompatible SD card.
The d3400 is not particularly sensitive to card speeds, and so I doubt that is the issue. Too slow a card and the camera will be slow and not very responsive, too fast a card and the camera will use it at the max speed it supports. Also, the camera supports pretty much every SD card out there, class-10, UHS-1, .5gb to 256gb, SD, SDHC SDXC. With 3 SD cards giving same error message, I would suspect the card slot in the camera needs to be repaired.
A couple times people have reported similar problems to me, it turned out they didn't know they were supposed to push the SD card all the way in until it clicks and locks in place. There's a spring-loaded locking mechanism you have to engage by pushing the card in far enough. To remove it, you have to push it in again until it clicks and ejects. (This is the way most SD and microSD card slots work. I don't have experience with Nikon DSLRs so don't know if they use the same mechanism.) They were just sliding the card in but not locking it in place. The poor connection caused the error messages.
You can also try peeking inside the slot with a flashlight to see if there's any dust or debris which is preventing good contact between the card and camera. If you see something, try using a can of compressed air to blast the debris out.