If you don't have a picture tube tester, this article explains how to check the filament with an ohmmeter to tell if it's a dud.
http://www.antiqueradio.org/FirstStepsInRestoration.htm
If the filament is intact, the tube may be dim, but it might be good enough to get you through the restoration, anyhow.
If you have zero experience working on old tube devices (radios, whatnot), a TV is not the ideal beginner's project. Skimming a couple of B/W TV restoration articles in this section should give you an idea what's generally required to get them working:
http://www.antiqueradio.org/restoration.htm
Regards,
Phil Nelson
Phil's Old Radios
http://antiqueradio.org/index.html