No output voltage at transimpedance amplifier with TL081
First, with only 20 &micro;A of input current and a 1 k&Omega; feedback resistor, you would only get 20 mV of signal when everything is working right.  Are you sure you didn't?

Second, if you really aren't getting a signal out, it probably has to do with how the amplifier is powered.  The TL081 needs significant headroom at both ends of its supply range.  If you used a single ended supply with ground being the negative side, then what you have is guaranteed not to work.  Since you left off the all-important power connections, we don't know what you did, and getting into details would be pointless.