I recommend using the number of genes on Affy array (those would be the smallest one). But before you should filter those 1370 genes from Chip Seq so they only contain the genes also present on Affy array. And you should use not probes, but genes, as there are several probes per gene. Then compute 1 - F(37, 652, x, X) + 0.5 * P(37, 652, x X), where x is the number of Chip Genes, X total number of genes, F(.) is cumulative distribution function and P(.) is probability for Hypergeometric distribution.

PS Anyways the P-value looks to be insignificant. Have you tried checking up-/down-regulated genes separately or, better, using GSEA as suggested by Devon Ryan?

Take as the total number of genes (N), the intersect of the genes you looked at via ChIP-seq (all of them in the annotation you used, though this will be a bit of an overestimate, realistically) and those probed on the array (N.B., genes, not probes, as pointed out by mikhail.shugay ). In R, that could be done with:

m <- matrix(c(37,652-37,1370-37, N-652-1370+37), ncol=2,
    dimnames=list(c("ChIP.Sig", "ChIP.NoSig"), c("RNA.Sig","RNA.NoSig")))
fisher.test(m)

You'll find that if N is ~18000 or bigger then this isn't significant.

BTW, you might consider something like GSEA, where you use those genes showing peaks in their promoter (or where ever else you're looking) as the gene set. This would have the advantage in that it looks at the genes as a group, rather than relying on individual significant adjusted p-values. One could easily consider even more complicated tests (e.g., what if many of the DE genes have promoters with low mappability?), but I'd probably avoid going really whole-hog without reason.