The NES Game Pak edge connector has three parts: the CPU part, the PPU (Picture Processing Unit) part, and the CIC (Checking Integrated Circuit) part. Bad CIC connection (pins 34, 35, 70, and 71) causes blinking, as you mentioned. But bad CPU connection (pins 2-15 and 38-50) freezes the Control Deck on a blank screen, and bad PPU connection (pins 21-33 and 56-69) causes scrambled tiles, vertical lines, and even freezes in some games.
The PPU failure mode doesn't happen on later Nintendo systems, which have no dedicated PPU bus; all video memory is internal to the console. (In fact, the NES and Neo Geo AES are the only major home consoles to bring the address and data bus for the PPU to the cart edge.) Nor can CPU and CIC connection failure be distinguished on Super NES and Nintendo 64, where the lock chip in the console holds the CPU in constant reset until the CIC pair authenticates. The Game Boy connector has only a CPU bus, and the system authenticates the cartridge by matching the logo data. (Incidentally, Sega's similar Trademark Security System got ruled unenforceable in U.S. courts; see Sega v. Accolade and Lexmark v. Static Control Components.) Nintendo DS and Nintendo 3DS use block storage, similar to CF or SD, with an encrypted bus.