Digital certificates

We recently moved our company to a new domain controller and new domain. (From nt4 to server2003)
Majority went smoothly, but we are having a problem where one user cannot access certain websites that need digital certificates.
He has the digital certificates on his pc(XP Pro) but when logged into the new domain, the websites do not recognise the digital certs.
I tried to export the certs when logged in to the old domain but i cant export the private key which I need to install the cert when logged into the new domain. Any suggestions as to how I might get around this without having to have the cert reissued?