Guys, reread his/her question. It's not that the light is completely on when the OP thinks it should be off, nor is it that the switch is lit. The OP says the fluorescent bulb is "half lit" with just the ends lighting up when the switch is off (and, I assume, on regularly when the switch is on). When fluorescent bulbs do this (when switched on) it usually means the ballast needs to be replaced.
In this case, since it's happening only when the switch is off, I think there is an unswitched hot going to the fixture. So, the switch seems to operate almost normally, but it's really switching neutral (because the switch is on the wrong conductor). If this is the case, a small amount of current could be leaking to ground in the fixture when neutral is "switched off", enough to cause the bulb to "half activate."
Matt