Multiple PCs simultaneously BSOD 0x0000000A

Hi. I have a bit of a situation at a construction site that I support. The guys there decided against having their own internet connection and decided to take up the offer to use the client's network. A cable was put in from a switch on their system to a switch in the site office cabin and distributed to a number of RJ45 sockets via a patch panel. The guys configured their laptops to connect via the client's proxy server, connected to the office LAN via the usual VPN client and everything was going great until suddenly, after a couple of days, all of the computers simultaneously blue screened and kept blue screening on every reboot attempt until the network cable was disconnected. After 10-15 minutes they'd re-connect the network cable and everything went back to working normally.
The laptops used were; three Dell Latitude E5440, one Dell Latitude E5430 and one Dell Latitude E5410. All run Windows 7 Enterprise x32 and all have, drivers aside, the same build. Oddly one of the laptops was unaffected by the crash. The old E5410 kept working while the others crashed. This makes me lean towards a driver related issue but as each machine has the latest driver for its specific model I don't really know how to tackle the issue. I don't particularly want to downgrade any of the laptops by rolling back drivers. Has anyone here seen this before? Are there any network events that can cause such behaviour? I'd be grateful for any ideas of where to start with this one.