Simple TIA PCB Problems
As @ThePhoton rightly points out, the bias current is the proximate problem. Tens of uA * M\$\Omega\$ = tens of volts output offset.

Note that the current noise is huge as well 2.6pA/sqrt(Hz) - it blows away the fine voltage noise performance of this amplifier by more than three orders of magnitude with a 1M feedback resistor. 

You can still salvage this by adding a JFET voltage follower to the input (inside the loop). Then the input current noise effect will be reduced by a factor of gm*1E6:1, and total voltage noise will only be slightly increased (assuming a decent JFET).