Many sources put the switch from LIBOR discounting to OIS discounting at some point in 2008, or perhaps a little earlier (the earliest I have seen is August 2007). It seems that this may be optimistic, and that the switch did not happen until a couple of years later, some time around 2010.
As far as I can tell, 10Y OIS were not often quoted until mid-2008 (Bloomberg has prices from 6th July) and longer term OIS were not quoted until the end of 2011 (Bloomberg has 15Y+ OIS quotes from 27th Sep 2011).
There is some overlap when the market built OIS discount curves, but long-term OIS swaps were not liquidly traded. What techniques were used to build the discount curve in the absence of OIS quotes?