I'm actually shocked at how many places accept the trust chain of my free SSL certificate from Gandi. Some browsers refuse my company's very expensive wildcard certificate from GoDaddy saying it's not trusted but trust mine from Gandi!
Their certs are issued by Comodo, which is a well established CA. And they are hardly free, their price is simply rolled into the domain registration fee.
Did you configure the server to send the intermediate certificates for your GoDaddy wildcard certificate? I've experienced similar problems in the past, but sending the intermediate certificate fixed it.
