Aside from reluctance which might encourage you to continue to build a <new virtual machine> based on openSUSE 11.0 (wouldn’t it be just as easy to create a new machine using 13.1?) and the fact that VMware Server itself has not been supported for… over 5 years?
The problem almost certainly is a virtual networking configuration since you have another Guest that works. Compare the two. You’ve made screenshots of your openSUSE configuration, compare with careful detail what your Windows networking configuration looks like.
Some common troubleshooting steps you should try…
Know that name resolution can be an issue on top of a working or non-working IP network so should be considered separately. So, Ping the DG by IP address and then beyond the DG <by IP address> and not names to verify basic networking is working. Once you’re certain there isn’t an IP address networking problem you can repeat your tests pinging names.
Try a different network. You’re configured for bridging mode at the moment. Try NAT (using DHCP). You can always switch back but you’re narrowing possibilities.
If the problem is DNS, verify the following file displays the correct ip address (run the following command)
If the problem is DNS, try a different DNS. You’re currently pointing to a DNS in you network. Remove or change the order of your DNS. In general, only the first entry will be used, the others are rarely if ever used.
Your main difficulty when considering upgrading isn’t the version of openSUSE, it sounds like it’s the version of MySQL you’re running. Although it might be possible to install and run an old version of MySQL, that also has its own issues but should be investigated. If that version of MySQL is still supported, then you probably won’t have any issue running that on a supported version of openSUSE. Assuming you’re running MySQL vintage used in 11.0, a major issue is that database connections are no longer created the same way so if you upgrade MySQL (again, highly recommended) you’ll likely need a MySQL Developer or Sr Admin who knows how to configure what you need.
Your screenshot is cropped, all I see is that you successfully pinged another address in your local network, nothing more.
Since you are running virtualization, it should be very simple to clone your existing openSUSE guest and explore a number of ways to upgrade… There is no reason to risk your Production Guests while you create an upgraded clone, fully tested.
You can upgrade step by step. If this is 11.0, it’s a long upgrade path. I don’t remember all the specifics over the years but around that version there was a special repository which supported skipping versions when upgrading, otherwise the advice then was the same as now… Upgrade one version at a time. So, you’d have to download DVDs for 11.1, 11.3. 11.4, 12.1, 12.2,12.3 (which currently is still supported) and optionally but recommended 13.1 (with 13.2 to be released shortly).
You can build a new 13.1 and install the appropriate version of MySQL you need. If necessary, you can even install an old version of MySQL no longer supported if necessary, it’s not a good solution but is still much better than your current situation.
Plan extensively. You should be able to do this with practically zero risk if your VMware Server has sufficient resources, and even if you can’t do your building and upgrading Guests on your VMware Server, you can do it on another machine running something like VMware Workstation… You just need to be certain that any new Guests are created specifying the version of technology used for VMware Server.