smc

We see that $1,2,3,$ and $4$ each appear in the ones, tens, hundreds, and thousands digit exactly once. Since $1+2+3+4=10$, we find that the sum is equal to $$10\cdot (1+10+100+1000)=\boxed{11,110}.$$ Note that it is equally valid to manually add all four numbers together to get the answer.