Thanks for the information.

Here's what I see.

You have disabled all of the standard VMware virtual networks. Why?

And that's part of your problem because:

You have no VMware virtual networks that have connectivity to the outside world with the exception of the vmnet2 bridged network (which doesn't get shown in the virtual network editor) which I do NOT recommend for your Windows 95 VM. Your existing vmnet0 is a true host-only network Unlike vmnet1, your custom network does not have connectivity to the host nor any way to route traffic to the Internet. It also does not have DHCP enabled, so you would have to manually configure the IP address within your VM - which is totally unnecessary .

All of these add up to why Internet Explorer is complaining - it can't resolve hostnames or connect to systems on the Internet because it has no way to get there.

This is what your virtual networking should look like. Note the NAT network vmnet8 - that's the one that you want to use in your virtual machine's configuration. It isolates your Windows 95 from the Internet, but still allows outbound communication. 

You need to introduce the TCP/IP protocol in the Windows 95 VM in order to connect to the Internet. The instructions in the link I posted are pretty easy to follow and you do not have to do any further configuration.

Trying to do dial-up or wi-fi (especially in Windows 95) is an exercise in futility. Stick with configuring a virtual wired networking and leave it at that.