How would the Airbus A320 PFD respond to failure of all pitot and AOA sensors?
The primary flight display¹:



is a single display, but it shows five separate instruments:


On the left, the speed tape. This shows the value from the pitot probe.
In the middle the attitude indicator. This shows attitude from gyroscopes. All gyroscopes are grouped in the “inertial reference unit”.
On the right the big tape is altitude. This shows the value from the static port.
The smaller tape at very right is vertical speed. It is normally taken from the inertial navigation system, which is part of the inertial reference unit, but can fall back to the static port.
On the bottom is compass. This shows the value from the inertial reference unit, which has drift automatically compensated by reference to magnetometer.


The angle of attack is not displayed anywhere. It is only used for stall warning, as part of the alpha-protection logic and for checking the weight set in FMGC.

For all the instruments, each instrument shows value from one input. The three pitot probes, static ports and inertial reference units each feed one of the three displays in the cockpit: captain's PFD, copilot's PFD and the standby instrument (which in the modern version looks like smaller PFD and is placed between captain's (left) displays and the centre display.

When any of the input fails, the computer will generate a warning (accompanied with the annoying cricket sound) stating that the values do not match, but it leaves it up to the pilots to determine which one is wrong. The pilots can then switch the displays to show the one they determined as trustworthy.

So:


If all pitot probes failed, the speed would show nonsensical values, but the attitude, altitude and heading would remain operational. The system would fall back to alternate law. There is an unreliable airspeed procedure where the aircraft is kept in safe speed range by reference to attitude and vertical speed. Failure to execute that procedure properly was an important part in the accident sequence of Air France flight 447.
If the angle-of-attack vanes fail, the stall warning and alpha floor protection will not work, but all displays would work. However, the system may actually not notice that they failed as evidenced by the accident of XL Airways Germany flight 888T. This was a test flight where they intentionally tried to activate the alpha-floor and it did not activate without any prior indication because the AoA-vanes froze due to improper wash.




¹ The image shown clearly is supposed to be Airbus PFD, but some elements like the protection indicators and the Mach number are missing. I just didn't quickly find better as this one is very readable.