Start with simple things first.

For example look for correlations between the binding of certain factors and the expression of the genes that are regulated by them. Count all the binding events (x) in a promoter region, then compute the average expression for the regulated genes (y). Do this for each timestep. Now you have two vectors x and y with equal number of values, what is their functional form is, do they correlate at all?

(there will be a fair amount of data shuffling/filtering involved)

With this you can quickly check that your data works at all and that you do indeed have all you need. From this you can then expand on.

I have always found the biggest problem of comparing ChIP-chip/seq binding regions with expression data is the use of gene symbols, i.e. whether the genes associated with binding regions also represented in the gene expression data (and visa versa).

So you could simply try intersecting ChIP-chip binding region coordinates (+/-) a threshold of your choice (say 50 or 100kb) with the probeset coordinates from the gene expression data.

For a more in depth and modelled approach i would follow Casey's suggestion.

Rattray, Lawrence, and Sanguinetti have been doing interesting work in this area. You may need to look around to see which of the various methods they have developed suit your needs, but you can try TFinfer for a start, since it is designed for E. coli.