You can also move the above bitcoin-qt file to another directory by itself, no other files from the archive are needed to run Bitcoin. You can be really fancy and add an icon for it.
Make sure that you successfully created a persistent directory for your data, that you can shut down and reboot and your Bitcoin wallet addresses and the current block count are still there (just booting the live cd will always forget anything you downloaded as it only uses a RAM disk.) Also use UUID, so that partitions will always be found even if you use different USB ports or a different computer:
http://wiki.tinycorelinux.net/wiki:persistent_home
If "trusted boot" is enabled, a computer will only boot signed code. This is being worked on by kernel devs, but it requires kernel code signed by Microsoft. This is more of a grab by Microsoft that no user wants, under the guise of more security.
Both of these "features" can generally be disabled in BIOS. Windows 8 certified systems are required to permit the user to disable Secure Boot.
now i'm having trouble booting to TC from USB despite checking boot loading order in bios. have you ever seen this inconsistency? this has been reported before.
which installer did you use? CorePlus, unetbootin? they recommend CorePlus but now my usb refuses to boot. funny b/c the one time i got it to boot to TC was after i used unetbootin to install. now that even won't work.