VE networking can be a bit tricky. Now that you are able to contact this VIP, what you need to verify is if your node entries for your security/connection servers are green. A few questions: are the view servers in the same subnet as the self-ip of the VE? If yes, ensure SNAT Auto map is enabled on the VIP. If not, you likely need to set either a default route or a static route in order to reach the network that they are in.
You want to make sure that your interface lines up over the whole stack, from vmware to the f5, and the f5 interface to the vlan to the self-ip. It sounds like you are fairly close.
If this still doesn't work, then I recommend using the shell on the f5 and running some ping and telnet tests to your View servers.