For the FAQ Booting LPC-Link2: This board is brand new, it has never worked before.
In the Windows devices and printers section, I do not see any LPC devices.
Your second option (... fails to enumerate...):
Microsoft Windows [Version 6.1.7601]
Copyright (c) 2009 Microsoft Corporation. All rights reserved.
C:\Users\istvanfi_b>cd c:\
c:\>cd nxp
c:\nxp>dir
Volume in drive C is System
Volume Serial Number is 2080-52B1
Directory of c:\nxp
11.07.2016 09:08 <DIR> .
11.07.2016 09:08 <DIR> ..
11.07.2016 09:09 <DIR> LPCXpresso_8.1.4_606
0 File(s) 0 bytes
3 Dir(s) 127,840,866,304 bytes free
c:\nxp>cd LPCXpresso_8.1.4_606\lpcxpresso\bin
c:\nxp\LPCXpresso_8.1.4_606\lpcxpresso\bin>boot_link2
Nothing to boot
c:\nxp\LPCXpresso_8.1.4_606\lpcxpresso\bin>boot_link2
Nothing to boot
c:\nxp\LPCXpresso_8.1.4_606\lpcxpresso\bin
I tried it with LPCboard disconnected, and also, connected. Same result.
In windows device manager, I do not see any LPC or nxp USB devices. All are from Intel, Microsoft, one is from FTDI, it's a USB-Serial converter.