算法的设计思想：
1）从左到右按位读入加数1，并存入栈1； 2）从左到右按位读入加数2，并存入栈2；
3）若栈1非空，则栈1出栈赋值给j1， 否则0赋值给j1，若栈2非空，则栈2出栈赋值给j2，否则0赋值给j2，若栈1和栈2均为空栈，则输出栈3.
4）j1加j2加进位（初值为0）的和的个位入栈3，十位赋值给进位，转3.
//顺序栈的实现
#include<iostream>
using namespace std;

#define OK 1
#define ERROR 0
#define OVERFLOW -2
typedef int Status;
typedef int SElemType;

#define MAXSIZE 100
typedef struct {
    SElemType *base;
    SElemType *top;
    int stacksize;
}SqStack;

//算法3.5 顺序栈的初始化
Status InitStack(SqStack &S)
{
      // 构造一个空栈 S
      S.base=new SElemType[MAXSIZE];    //为顺序栈分配一个最大容量为MAXSIZE的数组空间
      if(!S.base) exit(OVERFLOW);        //存储分配失败
      S.top=S.base;
      S.stacksize=MAXSIZE;
      return OK;
}

//算法3.6 顺序栈的入栈
Status Push(SqStack &S, SElemType e)
{//在栈顶插入元素e
    if(S.top-S.base==S.stacksize) return ERROR;        //栈满
    *S.top++=e;                    //元素e压入栈顶，栈顶指针加1
    return OK;
}

//算法3.7 顺序栈的出栈
Status Pop(SqStack &S,SElemType &e)
{// 若栈不空，则删除S的栈顶元素，用e返回其值，并返回OK；否则返回ERROR
    if(S.top==S.base) return ERROR;
    e=*--S.top;
    return OK;
}

//算法3.4取栈顶元素
SElemType GetTop(SqStack S)
{
    if(S.base==S.top) exit(1);
    return* (S.top-1);
}

int main()
{
    SqStack s1,s2,s3;
    SElemType e1,e2;
    char c1[100],c2[100];
    int a1[100],a2[100],i,j,j1,j2,j3,k,n1=0;
    cout<<"      大整数加法计算器\n";
    cout<<"* * * * * * * * * * * * * * * * * * * * * *"<<endl;
    cout<<"*        1----输入加数1                   *"<<endl;
    cout<<"*        2----输入加数2                   *"<<endl;
    cout<<"*        3----输出和                      *"<<endl;
    cout<<"*        4----输出差                      *"<<endl;
    cout<<"*        5----退出                        *"<<endl;
    cout<<"* * * * * * * * * * * * * * * * * * * * * *"<<endl;
    int choose=-1;
    while(choose)
    {
        cout<<"      请选择菜单号（0-4）:";
        cin>>choose;
        switch(choose)
        {
            case 1:
                if(InitStack(s1)==OK)
                {
                    cout<<"      请输入加数1：";
                    cin>>c1;
                    for(j=0,i=0;i<strlen(c1);i++,j++)
                        a1[j]=c1[i]-'0';
                    for(i=0;i<strlen(c1);i++)
                        Push(s1,a1[i]);
                    /*
                    while(s1.base!=s1.top)
                    {
                        cout<<*(s1.top-1);
                        s1.top--;
                    }*/
                }
                break;
            case 2:
                if(InitStack(s2)==OK)
                {
                    cout<<"      请输入加数2：";
                    cin>>c2;
                    for(j=0,i=0;i<strlen(c2);i++,j++)
                        a2[j]=c2[i]-'0';
                    for(i=0;i<strlen(c2);i++)
                        Push(s2,a2[i]);
                    /*
                    while(s2.base!=s2.top)
                    {
                        cout<<*(s2.top-1);
                        s2.top--;
                    }*/
                }
                break;
            case 3:
                while((s1.top!=s1.base)||(s2.top!=s2.base))
                {
                    if(s1.top==s1.base)
                        j1=0;
                    else
                        if(Pop(s1,e1)==OK)
                            j1=e1;
                    if(s2.top==s2.base)
                        j2=0;
                    else
                        if(Pop(s2,e2)==OK)
                            j2=e2;
                    j3=j1+j2+n1;
                    if(j3>=10)
                    {
                        j3=j3-10;
                        if(Push(s3,j3)==OK)
                            n1=1;
                    }
                    else
                    {
                        if(Push(s3,j3)==OK)
                            n1=0;
                    }
                }
                cout<<"加数1和加数2的和为:";
                while(s3.base!=s3.top)
                {
                    s3.top--;
                    cout<<*(s3.top);
                    
                }
                break;
            case 4:
               

        }
    }
    return 0;
}

不知道栈是否需要内容，楼主的栈感觉是个定位器，没有实际的容器存放东西；
输入3，应该是j3的问题，s.top指向j3，j3应该存放在静态区，而后指针自加加，应该指向不可访问的地方了就崩掉了。纯属猜测。

看错了，只看case 3得出楼上的‘好想法’了。楼主是没有初始化s3.。楼主务必要原谅原谅哥们

case 3:
                InitStack(s3)；
                while((s1.top!=s1.base)||(s2.top!=s2.base))
                {
                       ............
                }