The circuit diagram is a little hard to see but I think I've managed to follow what is connected to what.
To light any LEDs then 32 bits of data have to be written out of Port A bit 1.
To write a bit of data you do:-
Place data on RA1
Make RA3 high = 1
Make RA3 low = 0
The data you send will represent 1 row of LEDs.
As I’m a dinosaur, I count from zero upwards. Therefore the first bit is bit zero and the last bit is bit 31.
The first bit (bit 0) should be zero if the LED in the right most column is to be lit.
Bits 1 to 23 are the same for the other columns.
Bits 24 to 31 represent the row that is to be lit. Only 1 of these bits should be set to 1.
If bit 24 is 1 and 25 to 31 are zero then the top row will be lit.
After the 32 bits of data have been sent to the shift registers, you need to tell the shift registers to display what you have sent. You do this by strobing RA2.
You do this by
Making RA2 high
Making RA2 low
So, to light up the whole display you would do the following.
Send the data that represents the top row as the first 24 bits.
Send 1000000 as the next 7 bits.
Strobe RA2
Delay a short time.
Send the data that represents the second row as the first 24 bits.
Send 0100000 as the next 7 bits.
Strobe RA2
Delay a short time.
.
. do rows 3,4,5&6
.
Send the data that represents the seventh row as the first 24 bits.
Send 0000001 as the next 7 bits.
Strobe RA2
Delay a short time.
Repeat the above.
HTH
Mike.