Caeser Shift

[sebajun]

Hey guys, I've been practising my C before the new Uni semester starts and I'm having a bit of trouble with this program,

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#define MAX 100

void shift(char string[], int len);
void print(char string[], int len);

int main(int argc, char *argv[]){
    char string[MAX];
    int input;

    printf("How much would you like to shift by?:");
    scanf("%d", &input);
    printf("Now input your string: ");
    scanf("%99s", string);

    shift(string, input);
    print(string, input);


    getchar();
    return 0;
}

void shift(char string[], int len){
    int i;

    for(i=0;i<strlen(string);i++){
        if(string[i] > 'z' || (string[i] < 'a' && string[i] > 'Z') || string[i] < 'A'){
            string[i]=string[i];
        }else{
            string[i] = string[i]+len;
                if(string[i] > 'z' || (string[i] < 'a' && string[i] > 'Z')){
                    string[i] = string[i]+len-25;
            }
        }
    }
}

void print(char string[], int len){
    printf("\nYour string when shifted %d places is: %s\n", len, string);
}

Firstly, when I use "fgets(string, MAX, stdin), instead of "scanf("%99s", string", it totally skips the user input when it compiles, and I don't know why.
The second problem lies in that some inputs don't come out the way I like, for example;

"Hello!" -- when shifted 1 places comes out as "Ifmmp!" which is to be expected.

"Cry "Havoc!" and let slip the Dogs of War." Comes out " -- -- when shifted 5 comes out as "hwj" --- I'm guessing this would run better with "fgets"

"IBM" -- when shifted 25 places is "b[f" -- I can see why this happens I just can't figure out a way to fix it.

Would be great if I could get feedback on either of these two problems, I'm exhausting enough time as is.