The program:

DEFDBL A-Z
OPEN "8primesb.txt" FOR INPUT AS #1
'OPEN "8primes2.txt" FOR OUTPUT AS #2
mindiffdg = 999
CLS
DO
   LINE INPUT #1, l$
   a$ = MID$(l$, 2, 3)
   b$ = MID$(l$, 7, 3)
   c$ = MID$(l$, 12, 3)
   a1 = VAL(LEFT$(a$, 1)): a2 = VAL(MID$(a$, 2, 1)): a3 = VAL(RIGHT$(a$, 1))
   b1 = VAL(LEFT$(b$, 1)): b2 = VAL(MID$(b$, 2, 1)): b3 = VAL(RIGHT$(b$, 1))
   c1 = VAL(LEFT$(c$, 1)): c2 = VAL(MID$(c$, 2, 1)): c3 = VAL(RIGHT$(c$, 1))
   IF a3 + b2 + c1 = 4 THEN
     IF a1 + a2 + a3 = 11 THEN
       IF b1 + b2 + b3 = 17 THEN
        IF c1 + c2 + c3 = 5 THEN
           PRINT a$: PRINT b$: PRINT c$
        ct = ct + 1
        END IF
       END IF
     END IF
   END IF
LOOP UNTIL EOF(1)
CLOSE 1
'CLOSE 2

PRINT ct

goes through the output from the original program and finds:

641
809
311

Note that it was not necessary to check every total. The requirements were added as necessary to narrow the answer to one solution.