some laptop and desktop keyboards have multi-purpose F1-F12 keys along the top of the keyboard. Those keys are designed to interface with the computer in two ways. they can function as standard F1-F12 keys, OR they can perform a specific function (FN) related to the specific setup of the particular computer like volume control or brightness control etc. BUT they cannot act as both types of keys at the same time.
Those F1-F12 keys often will be set to perform their specified functions by default but, as with SH3 or other games if you want to set them to run as standard F1-F12 keys you have to make a change.
often on your keyboard on many laptops and newer desktops there will be a key, usually in the lower left labeled "FN" meaning function. OR you will have a similar key called "FN LOCK"
FN LOCK works like caps lock or num lock and LOCKS the F1-F12 keys into their predetermined functions such as volume control or brightness control etc. this does you NO good with PC gaming.
If your computer has this "FN LOCK" button, and your F1-F12 keys arent working in game... its because the function lock is enabled. to disable it, simply press the FN LOCK button to disable function lock and your F1-F12 keys should behave as normal F1-F12 keys
if you have a FN button but it doesnt say FN LOCK... often times there is another key (usually the esc key) with a lock symbol... if you press FN and this key with the lock symbol together this will disable function lock and return the F1-F12 keys to normal operation.
try that, and report back