Let's see if I have the right idea ... to clarify things again.
You have LXDE installed to the SSD. You have various VMs which run on top of it.
When booting LXDE you get a prompt/question box asking about which internet connection you wish to use.
Regardless which of the two you choose, you do not get a reliable (or any) internet connection.
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I'm sorry, but I have no idea where this prompt/question is being generated from.
I have never seen this on any PCLOS install I have done.
I would dearly love to know what is producing this question. So if anyone has any suggestions, please enlighten me, as I am stumped.

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On the understanding that your LXDE install is fully updated, you have the option of installing a newer 'test' kernel from the PCLOS testing section.
This would be much easier than d/loading another full OS.
On first boot after install, extra time is taken to build some modules. Subsequent boots should be normal speed.
If you wish to try one of the newer kernels ---- which does not interfere with your ability to boot your existing kernel in case it does not work well for you. --- then we can give you instruction.
Essentially it involves enabling the testing section in Synaptic, searching for the kernel package, installing the selected one, along with the one other package it brings in as a dependency, and immediately disabling the testing section again.
When that is done, reboot using the default boot option, which will be the new kernel.
Check your internet connection.
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One last question ..... To which of the two network connections is the ethernet cable attached?
The Intel 82579V has many reports on the net about dropping connections .... even with Windows. Here is one example ...
This problem was bugging me and after a number of false starts my solution has been to go into the advanced tab on the 82579v and select gigabit master slave mode and under value select force master mode. It intially dropped me down to 10 mbs FD but once I reset the speed to 100 mbs FD I have had no problem since. I am not runnig a gigabit router, it's a Westell 7500.
http://forums.hardwaresecrets.com/intel-82579v-gigabit/7648/2The Realtek 8111F appears to be supported by the rt8169 driver in Linux.
So I have this as a suggestion .....
Delete through PCC - Network & Internet all the existing NICs.
Immediately after that, set up one ..... select whichever you have the ethernet cable attached to, and go through the settings accepting all the defaults.
Check to see if it works.
If it does not, then back into PCC, delete it, and create a new connection using the other one (having changed the cable from one to the other).
Check to see if that works.
I know that seems like duplication of previous effort.

The newer kernel might make a difference with this r8169 driver.
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I continue to wonder where that question/prompt is coming from .....
