Client Connection Issue with SSL Cert

Before digging into potential SSL issues, I'd start at the basics. If you configure the VIP for port 80 HTTP with no SSL profiles, does it work?

If it works, and you re-enable client side SSL/HTTPS, how does it fail? If you place a tcpdump capture on the server side of the proxy (between the F5 and the server), do you see any traffic? If you see client traffic then there's a good indication that client side SSL isn't the problem.

If you don't see server side traffic, do you see anything in the LTM log? If you enable debug for SSL, do you see anything in the LTM logs? In your client SSL profile, do you have a server certificate AND corresponding private key configured? You could also run an ssldump on the client side interface to see if there's an issue in the handshake:

ssldump -AdNn -i 0.0 port 443 and host [IP of VIP]

This will show you the cleartext portion of the SSL handshake. If there are any errors in the negotiation, those errors will show up here.