I use Bridged on my T510, and L530. Both work in VBox under win 10.
A couple of things to check:
Under Attached To: make sure that it is the device that is being used by the host system. If there are two possible devices (wired, and WiFi), attach two Adapters, one to each adapter, but then you have the problem of determining which one to use in the guest.
Under Network Advanced, make sure that Cable Connected is checked. (this is the virtual cable between the virtual machine, and the NIC).
Make sure that the driver, in the guest, matches the device that is emulated. I use the MMLEM Multimac driver, with the Intel PRO/1000 MT Desktop device.
It is possible that your router has used all of the DHCP addresses that it is configured to use, so it won't assign any more.
Try "DHCPSTRT -i LAN0" (no quotes) from a command line, after you get it booted. It is possible that it is attempting to get an address, before it all gets started properly.
You could try using a fixed address. You may not want to leave it that way, but it may show something.
HTH...