I don't recommend linear interpolation of DFs and the swap rates you are applying this to are either against 12M libor which is illiquid or you are not accounting for Quarterly or Semi-Annual floating sides. And what I'm going to suggest uses a single curve framework which is long outdated. But that being said and given the nature of what's been asked...
You have adopted the simplistic formula:
$R_{tenor} = \frac{1-D_{tenor}}{\sum_{i}D_{i}}$ You need to make an assumption about your model, since otherwise it is under parametrised. Lets say that you assume the rates are linearly interpolated then the problem is probably trivial to determine the DFs by bootstrapping, after you calculate the 2Y and 3Y rate.
If instead, you want to have linear DFs between 1Y and 4Y then you have the following:
$$D_1 = D_1, \; D_2=D_1 + 1/3 (D_4-D_1), \; D_3 = D_1 + 2/3(D_4-D_1), \; D_4=D_4$$
Inserting that into the equation for the 4Y rate gives:
$$ 1.03\% * (2 D_1 + 2 D_4 ) = 1 - D_4 $$