The answer depends on what you mean by the average impact of $D$ on $Y$. Each of the words "average" and "impact" are ambiguous.
"Average" has to be relative to some population. The average height in the US is different from the average height in the NBA. "Impact" can be in units, how many dollars/gallons/whatever does $Y$ increase when $D$ goes from 0 to 1; it can be in percents, how many percents does $Y$ increase when $D$ goes from 0 to 1; or it can be in some other sense (though units and percents are the most common).
Suppose you are interested in the average percent impact of $D$ in your sample. You calculate that as follows. The effect for each observation in the population is:
\begin{align}
\text{Effect}_i &= \beta_0 + \beta_4 yr_{1990,i} + \beta_5 yr_{1995,i} + \beta_6 yr_{2000,i}
\end{align}
And the average percent effect in this population (i.e. the population consisting of your sample) is just the mean of the above:
\begin{align}
\overline{\text{Effect}} &= \beta_0 + \beta_4 \overline{yr_{1990}} + \beta_5 \overline{yr_{1995}} + \beta_6 \overline{yr_{2000}}
\end{align}
This is subject to the usual caveat that coefficients on dummies (and non-dummies, for that matter) in log regressions can only be interpreted as percent effects as long as the coefficients are less than about 0.2 in absolute value. Otherwise, you have to do the calculation properly.
On the other hand, if you want the average effect of $D$ on $Y$ in units, you do a different calculation. The effect of $D$ on $Y$ for a single observation is:
\begin{align}
\frac{\partial Y_i}{\partial D_i} &= \left( \beta_0 + \beta_4 yr_{1990,i} + \beta_5 yr_{1995,i} + \beta_6 yr_{2000,i} \right)exp(\widehat{lnY_i}) \left( \frac{1}{N}\sum exp(e_i) \right)
\end{align}
If this formula is unfamiliar to you, you might look at my answer here, for example. Or, you might search the site for the re-transformation problem or Duan's smearing estimator.
Then, if, again, you are interested in the average effect over your sample, you just take sample means:
\begin{align}
\overline{\frac{\partial Y}{\partial D}} &= \left[ \frac{1}{N}\sum \left( \beta_0 + \beta_4 yr_{1990,i} + \beta_5 yr_{1995,i} + \beta_6 yr_{2000,i} \right)exp(\widehat{lnY_i}) \right] \left[ \frac{1}{N}\sum exp(e_i) \right]
\end{align}
Again, there is a caveat. Since we are using a derivative (i.e. approximation) here, it's important that the individual-level percent effects, $\left( \beta_0 + \beta_4 yr_{1990,i} + \beta_5 yr_{1995,i} + \beta_6 yr_{2000,i} \right)$, not be bigger than about 0.2 in absolute value. If they are, then you have to do something else.
