RE: 5510 Thunderbolt Works With Linux Mint17, Win10 but not with Win7
Did you install the chipset driver?
That should get Thunderbolt working.
Note: The current Skylake platform is the last one that will have Windows 7 support, so you may want to (or have your organization) reconsider running Windows 7. Once Kaby Lake arrives, Windows 10 is the only version of Windows that will run -- this, just for future reference.