I'm on the XB so can only guess at the PS process. Clearing a console's cache is clearing the short term memory of your system (not the hard drive as this is long term memory). For the XB this is done by pressing and holding the power button until the system shuts down (a normal quick tap of the power button puts a system onto standby and not really off). Try see if that works for you and also unplug from the mains (and if possible the power pack) for 5min then log into Destiny. You should know if it works as your console will take longer than normal to power up.