How old is it? What model (gray, blue & white)?
If it is older than 6-7 years, then I fear it's gone. CRTs usually have a lifespan of 5-8 years (about two, two and a half computers) in my experience.
My guess it's the transformer or the electron gun itself. If it is, it's dead, Jim. But since you're sure, all cables are connected properly, I wouldn't hold out too much hope to revive it. If you want an equivalent of a 21" CRT, I suggest you take a look at 19" LCDs which have the same viewable area. If you want/can spend more, a 20" wide-screen tft would be a nice thing

Do a search to find out what options you have.