I have my certifcate issued by "TC Trustcenter" in a CER file. Thunderbird 3.0 needs it as a PFX files. So I installed the CER certificate with the Internet options in the Control Panel. Thereafter I exported the certificate including the "private key" and "all certificates in the certification path" to a PFX file.
After importing this certificate with Thunderbird I still cannot decrypt the mail sent to the mail address of the certificate. What else must I do to use the private key? The certificate is valid since I decrypted the mail already on another computer using Outlook. I verified the certificate serial number to ensure that I use the same certificate.

.cerfiles only contain the public part of your certificate -- the private key has been stored by Windows directly, at time of sending the certificate request. – grawity Dec 3 '11 at 13:04