I doubt that the remote is the problem.  The On/Off button should send the same signal every time it is pressed.  Oddly, the manual on page 8 says: "You can only turn the projector on/off with ON/STAND-BY button on the projector."  Page 15 says that the remote can also turn it on, as we certainly would expect.

Page 17 shows an on screeen display that has a menu item "Advanced".  Perhaps there is some kind of power option buried there.  

As with most projectors, the unit will not turn on until it has cooled some from previously being on.