L7805CV - Circuit not pulling expected current when powering from Voltage regulator
For powering from 5V:

The dropout for this regulator is 2V so that means you need at least a 7V input to run the regulator. Since USB is only 5V the regulator doesn't have enough voltage to turn on the transistors inside of it to supply current. 

You can buy regulators with lower dropout (like 50mV, I think they go as low as 20mV), however that would mean you'd need at least 5.05V. Another caveat is the usb cables usually have a drop from resistance so if your sourcing 100mA's then you'll get 4.9V or 4.8V at the end of the cable. 

If you really need 5V regulation, you'll need a DC DC converter. 


Source L7805CV datasheet

For powering from 12V:

The circuit should regulate to 5V, you have enough dropout. You may want to check the input to make sure you have at least 7V, if the battery has too much internal resistance (like on a 9V alkaline battery) then you won't be able to pull much current from it. 

A car battery should be able to source enough current, but check the output to ground anyway.

You may have the regulator wired wrong it shouldn't power anything from 5V so double check the pins with the datasheet.