Peter Flom's answer makes a good point, but strictly speaking, the situation is more complicated than that. Treatment 2 is administered conditionally on the failure of treatment 1. Suppose the probability of success with treatment 1 is $p_1$, (respectively $p_2$ for treatment 2.)
Each patient who receives treatment 2 and is cured thereby contributes $(1-p_1)p_2$ to the likelihood. With 4 patients, that gives $(1-p_1)^4 p_2^4$.
You could then maximize the likelihood for $p_1$ and $p_2$ and compare, via a likelihood ratio test to the likelihood when $p_1=p_2$.
However, in your case, since no one was cured by the old treatment, MLE's for $p_1$ and $p_2$ are 0 and 1 respectively and that test will breakdown. But there is another way:
Assuming $p_1=p_2$, the MLE for the NULL model is $p=0.5$. The probability of getting what you got, or worse (only there isn't any worse) is then $0.5^8=0.004$.
However 4 patients is pretty small ... and from a design perspective, I would like to see a randomized trial. Or at least a cross-over. I don't know what the illness is, but if it were the common cold, that's exactly the result you would get if you applied two bogus treatments. The first would fail, and the patient would get better in time.