The only such polynomial is $p \equiv 2 x^3 + x + 4$, which clearly satisfies the problem statement. If the degree of $p$ is more than $3$, with the leading term being $a x^b$, the condition of all coeffients being nonegative givens $p(10) \geqslant a 10^b \geqslant 10^4$, a contradiction. Hence $p \equiv ax^3 + bx^2 + cx + d$ for $a+b+c+d = 7$. Since every coefficient is less than $10$, this means that the equality $2 \times 10^4 + 10^2 + 4 = a x^3 +bx^2 + cx + d $ implies $(a,b,c,d) = (2,0,1,4)$, since no term can \uv{overflow} into the next, and we are done.