There really are only 3 parts to a SSL cert being used. It's usually easiest to check every step.
1) Make sure your apache config (or IIS/whaever) is correct. Did you correctly setup the SSL in the config? Are you being presented with a certificate at all? Or are you completely unable to connect to port 443 on that machine?
2) Make sure you're using the correct certificates. It's not hard to mix up the private key and public key with each other, or with a self-signed cert. Apache will throw an error if you mix the private & public keys... but none with self-signed certs. If you're able to connect to the site and are presented with the wrong cert, it's a good indication that your site is simple misconfigured with the wrong certs & you need to switch them with the correct public & private keys.
3) Certificate validity. Make sure the certificate is valid. Valid includes a few simple checks. #1: Is it expired? I've actually run into a glitch with one vendor who issued a certificate that was already expired. #2: does the subject name match the URL? Getting a cert for https://www.domain.com and browsing to https://domain.com won't work. #3: is really an appendage to #2... If you got a wildcard domain, you still have to match the domain suffix. i.e. *.domain.com won't match for *.domain2.com.