Wake up a PIC from sleep using Timer1 Interrupt
Well, the reason why it doesn't work is the value you have chosen on both your attempts for the T1CON register.

T1CON = 0b10110101;
T1CON = 0b00110111;




The problem is with the T1OSCEN bit, where it is always set to '0'. The T1OSCEN lets you enable or disable the oscillator that the Timer1 is using when you want it to work on an external crystal.

If the oscillator is disabled, like in your case, the Timer1 cannot work on the external crystal.

Check also the Timer1 block diagram, where it will be clear: