The PIC does not start its program.

[skimask]

Not right now, skimask.
The issue is that the pic is not even starting its programme.
I want to give you more information. When voltage is being applied to the circuitry, these levels are given on the pic's socket:
RA3 = Undefined, Floating
RA4,RA5,RB2,Vdd,RB5 = 5.01 Volts
RA7,RA7 = OSC

That's EXACTLY the issue. If you break it down into it's simplest form, you can probe around, put parts in, pull parts out, play around, without worrying about anything.
And again, YOUR program only execute ONE TIME. Are you going to sit there and keep pressing RESET while you mess around trying to probe?