Your link came up empty ("not found") but I suggest you look at the schematic for your particular power supply
and find the C2 capacitor. The numbers you read seem to be production numbers.
There's recapping info for most of the Atari power supplies here
, but I didn't find that specific ASP34 revision you have. Maybe the differences aren't that great.
I don't know what kind of capacitors Frys sells, but don't just settle with the cheapest generic one you can find the easiest.
I suggest you go for high quality, brand name capacitors from reputable component dealers if you want to recap. Exxos sells complete "recapping kits" where he's picked out the components you need, saving you the hassle. I think this is the one you want
although there's no mention of the revision number. Better ask Exxos before you order.
Although only one capacitor in your PSU appears to be non-working I would for sure replace them all. They've all aged, their capacitor values have surely changed since they were new and you never know when the who thing breaks down, perhaps because of one capacitor which presently seems OK. Replace them all with high quality components and be done with it
I've just posted a "how to" guide on recapping the Mega STe power supply
. Most of the information (obviously apart from the parts list) should be applicable for recapping other Atari ST power supplies as well, so I suggest reading through it if you've never done this sort of thing before (or even if you have). Good luck! UPDATE
: I've just downloaded the ASP-34 schematic from the above link and it reads the ASP-34-1 meaning it's your exact PSU revision.
Sorry, I should have read through your previous postings a little better because you're not referring to the usual components which need recapping (electrolytic capacitors), and I see that C2 in the schematic is valued at 0.002uF/400V (or 2nf/400V) which corresponds well with the "222M" marking you found. According to this online capacitor calculator
it translates into 2.2nF/400V and I believe you're looking for a ceramic capacitor with those markings, but don't quote me on that. Maybe someone else can confirm that.