Grounding sheds and garages
Nope, the grounding rod is not a substitute for a ground wire back to the main service.  It simply will not do what you desperately need it to do.  

In fact, any electrical fault when the grounding system should be helping you, instead the entire grounding system gets lit up at mains voltage!  Now every light switch cover screw, every bit of conduit, the service panel itself is electrified. 

The two grounds have different jobs.  Remember, current travels in loops, and it wants to return to source. 


The grounding rod returns natural electricity (lightning, ESD) to its source, which is the earth.  
The ground wire returns human-made electricity back to its source, which is the neutral lug on the transformer on the pole.  It's supposed to do that via the neutral wire, but the ground wire is there on the hopes that some faults can return via the safety ground to the main panel's bonding wire, instead of via a poor human and some convoluted path back to source. 


They are not interchangeable because dirt is a poor conductor of electricity. 



Now the best way to safe this thing is to put a GFCI breaker on the breaker in the main panel.  GFCIs do a pretty good job of rendering human electricity safe.  

Once the GFCI is on board, having an isolated ground via your ground rod scheme would actually help the GFCI work.   A ground fault in any of your equipment will still light up your grounding system with lethal voltage, but the GFCI should intervene before enough current flows to actually hurt you.

Of course this isolated ground would do a fine job of returning natural electricity to source.