You could use liftOver which isn't always great.
Whenever I encounter this (especially NGS data readily available on the SRA), I often just get the raw files (e.g. fastqs) and re-align/re-map.
In your case (arrays) it may be a bit tough. Not impossible though, as I recently took some old yeast DNA/RNA microarray data and updated it to the newest genome. Just requires the right data (like DNA for normalization) and a good understanding of the entire process.
A last resort/alternative is to align your new data to the old genome to be able to make comparisons. This isn't ideal but works in cases where upgrading one source isn't possible or is a HUGE amount of time/effort. I've done this for a few fly experiments where all the available/previous data was done in dm3. All the old genomes can generally be found on http://archive.ensembl.org .