That PSU will work for you just fine, as it has a 20+4pin mobo power connector. It is impossible to tell what yours is from that picture, but all you have to do to make sure, is disconnect the power cord and count how many wire connections there are. It will either have 20pins or 24pins, either of which will work just fine with your PSU.
Its a 24 pin from an hp slimline s3720y. I know hp did some weird things with the s series. That some used a small version of a 24 pin. As i look threw several sites selling adapters and i didn't find my the s3720y on the list. I'm not sure if they used the small version on all or only some.