Where am I going wrong with LM317 power supply circuit?
There are a few issues here.

The first issue is that, as others have said, your circuits are not identical.  An equivalent to the first circuit would be:







simulate this circuit &ndash; Schematic created using CircuitLab

Note that the battery is in parallel with the first capacitor (acting as a filter to smooth out ripple input and improve stability).  A capacitor in a DC circuit acts as an open circuit (ideally), which prevents current from flowing in the configuration you have.

The second thing to note is that C2 is an electrolytic capacitor, and you have used the symbol for a variable capacitor.  Electrolytics are constructed differently than normal ceramic and film capacitors, with two main differences:


They have a much higher capacitance by volume
They are polarized and must be installed in a specific direction relative to voltages


One final thing to note with the LM317 is that the schematic representation can be a bit misleading for the common TO-220 package.  The schematic symbol lists the pins as In/Adj/Out going from left to right, while the device itself has the pins as Adj/In/Out in the same direction.  Make sure you connect your pins correctly!

Edit: updated schematic to reflect the possibly-different grounding scheme used in the topmost reference schematic.