Bias voltage of non-inverting op amplifier drops to 0 when input signal connected
I see you had the input capacitor shorted but you will likely hit another problem with this op-amp.

There is a significant problem in running your amplifier at a total power rail of only 5 volts and it is listed on page 5 of the data sheet. The table on page 5 states that the input common mode range is (V-) + 2.5 volts to (V+) - 2.5 volts and this leaves you with an input range of nothing when running from a 5 volt supply.

If you are just building a one-off you may get lucky but, if you are building for production then either increase the supply rails or choose a different op-amp.