You measured the voltage incorrectly. At the fuse it is AC not DC, so measuring to ground isn't a valid measurement.

You start at the power supply. Remove the connector that goes to the CPU and then power up the game and make measurements. If the power measures good, and the game isn't booting, that is, you do not see control lights you have more work to do. These games have connector problems.
Does the CPU have corrosion from the NiCad battery? Has the corrosion followed to the CPU to driver board connector, and maybe even down to the driver board?

You will have to replace electrolytic caps on the power supply or replace it with a modern design replacement. If the CPU has a problem, I would sell it and buy a Ni-Wumph board. It just isn't worth the time and trouble of attempting to repair a Gottlieb system one CPU. Then if it breaks after a few hours of play you go through the trouble again.

Also, the power supply is the small board on the left side located in the back box, not in the bottom of the cabinet under the playfield.

http://www.pinwiki.com/wiki/index.php?title=Gottlieb_System_1

Good place to start with regard to system 1's.

With a real old System 1 that has not been maintained, look close at the MPU and see if it has corrosion all around the lower left corner and that the battery is not leaking all over. If you have either of these things, then you have a lot of work ahead.

Then follow the wiki and check power into the MPU.

Make sure you do all the ground mods too.

Be sure when measuring AC you do not ground your meter to test. You are testing those AC voltages across BOTH AC inputs/outputs correct?

You still are measuring incorrectly. It is highly unlikely the transformer is a problem.

At the power supply, remove A2P2 and A2P3 (top and side connectors) Power up.

Set your meter for AC.

On the bottom connector A2P1 that remains connected to the power supply measure:

between pins 1 and 2 and you should read 11.5 VAC
between pins 4 and 5 and you should read 14 VAC
between pins 6 and 7 and bingo you have 69 VAC.

Be care you don't short between pins making the measurements. Pin 1 is left most on the connector.

Now move to the power supply outputs - all are DC.

Top connector location A2P2:

Pins 1/2 and ground should be 5 VDC set voltage to 5.1 VDC using POT top right.
Pins 6 and ground should be -12VDC (negative 12VDC) Needed for obsolete spider chips
Pins 4/5 are grounds

Side connector location A2P3 (display voltages will not prevent MPU/CPU boot)
Pin 1 to capacitor C6 ground 60VDC
Pin 3 to capacitor C6 ground 42VDC

Follow PINWIKI after doing power checks and ground modifications

Given your results it appears your transformer is short on voltage for the displays. What about the other voltages? The function of the game is the sum of all voltages being correct.

The display voltage problem will not prevent the game from booting and playing.

It is possible the tranformer is wired for 220AC input depending upon where you acquired the machine or it's previous background. Which would account for 35VAC vs 69VAC. However, the other measurements would also have to be 1/2 of expected value. Are they?