The most common cause for the Timer to Stop After 7 Seconds on a Precor Elliptical is NO RPM Feedback.
Knowing the status of the unit from its last use as well as the last service or part replacement is a great place to start.
Check the connection of the speed sensor to the lower board. Reset connection if necessary.
Check the magnet. The magnet is located on the user's right crank arm on versions 1 and 2 and the user's left on version 3. The magnet passes the speed sensor with each revolution of the crank arm. The magnet should be installed so that its south pole is facing the speed sensor. You can check the magnet polarity with another magnet that has marked poles or a compass. The north pole of the marked magnet or the south-facing needle should be attracted to the magnet. Correct magnet installation if necessary.
You may also check the spacing of the speed sensor to the magnet. The spacing should be 1/8" to 1/4". Adjust if necessary.