Apologies for the basic question, but somebody will have to ask it ... Did you actualy "Capture" the clip, or did you just "Log" it?
When you use Log and Capture you can do either, or both. If you mark an In and an Out point and then press "Log Clip" then exactly what you describe will happen ... the clip will be "logged" in the Browser window but will not yet be captured. It's icon will be that of an Offline clip. If you press "Capture Clip" then the tape should preroll and play, and FCP should capture the clip.
Or is that what you're doing but it still appears "offline" ? In that case, can you verify whether the media was actually captured and the clip exists in the capture scratch, but for whatver reason has not linked with its masterclip item in FCP? OR is it a display glitch? If you double click the "offline"clip does it load correctly in the viewer?
Cheers
Andy