The LEDs on a standard keyboard are controlled by software in the BIOS. They usually flash when an initialization code is received but there is no obligation for them to do that.
For example, when 'NumLock' is pressed, the keyboard sends a command to the BIOS which sends a command back to turn the LED on. If there is no communication it won't work.
PS/2 keyboard protocol is the same as used in the days of 5-pin DIN, it uses two open-collector lines, clock and data. USB needs two data lines and regenerates the clock itself so they are not inherently compatible. Beware that some USB to PS/2 (and reverse) adapters actually have a controller built into them, a direct connection wouldn't work.
Brian.