Radio Shack thermo hygro sensor model 63-1090 reads everything except the outside temp

take it back as it is not fit for the purpose
have it checked under warranty

Relace the thermo senser

Did you reset the sensors after replacing the batteries? Bring the sensor inside and close to the main unit. Replace batteries on both units. Use a thumb tack and stick it into small reset hole near battery compartment to reset both units. If that doesn't work, your sensor needs more troubleshooting or needs to be replaced.

Mine reads HH.H on outdoor after a hailstorm. The wire was broken to the outdoor sensor.

It sounds like it is working properly.

I tried this and it worked fine
FACTORY RESTART:
A Factory Reset will erase the connection between the Display and the Thermo-hygro sensor and allow a fresh connection to be re-established. It is recommended to have the display and all sensors 5-10 feet apart for this restart.

ENTER PROGRAM MENU
Press and hold the SET button until you enter the program menu. Press and release the SET button until you see 'rES oFF' flashing.

FACTORY RESET ON
Use the UP ARROW key or DOWN ARROW key to turn rES on.

CONFIRM & COUNTDOWN
Press the SET key to confirm and a countdown timer will begin counting down from 127. When the timer displays dOnE, you must remove the batteries from the display for 10 minutes

REMOVE BATTERIES FROM THERMOHYGRO AND RAIN
While the batteries are out of the display, also remove the batteries from the Thermo-hygro sensor and the Rain sensor. Wait 15 minutes.

GENTLY KEY THE WIND SENSOR
Gently key the wind sensor one time to activate the sensor.

INSTALL BATTERIES INTO THERMOHYGO AND RAIN
Insert fresh alkaline batteries into the Thermohygro sensor and Rain sensor make sure to check polarity with the markings on the battery cover and inside the battery compartment. Wait 2 minutes.

INSTALL BATTERIES INTO DISPLAY: Insert fresh alkaline batteries into the Display. Make sure to check polarity with the markings inside the battery compartment
15 MINUTES: Wait 15 minutes for the outdoor weather data to display. If the outdoor data displays dashes after waiting for 15 minutes, repeat the steps of restart.
AZ Road Runner

This may be a wiring issue as the sensor is electronic in nature. Any loose wiring may cause the voltage across the sensor to differ resulting in an inaccurate reading.

Try this site:

http://www.chaneyinstruments.com/pdfs/00606.INST.09.VIEW.PDF

I've had a similar problem with another model, an Oregon Scientific Model IWA-80055 Wireless Thermo Clock, in which when I replaced the batteries in the remote sensor, the clock would not read the temperature from the remote sensor.
I found it fairly consistent to solve this by taking a battery out of place in the clock and putting it back in.  Unfortunately this also messed up the clock's time and date.  This is also in the instructions catalogue for the device, check and see if yours gives a similar solution.