It's probably not the CRT itself. It's the board that provides the high voltage needed to operate CRTs. The board is placed vertically along the side of the CRT (I can't remember if it's the left or right side). On the other side is the power supply board. Because of the high voltage that is present (even if the iMac is disconnected from power), it is dangerous poking around in there.
If it's so, can I send it to an apple service center to get the CRT replaced?
It will probably cost more to have it fixed than the value of that model working. A business that repairs CRT TV sets may be able to replace that one part on the analog video board that is usually faulty - the flyback transformer - and do it for less cost. If you replace the whole board, the replacement will be old (and maybe used) and may also go bad soon.
I would save your money and get a newer Mac. For the time being, if you have an old VGA display or can get one cheaply, you can connect it to the connector on the internal chassis and keep using that iMac as is. You need one of these adapters (or something like it).
[Apple Mac to VGA Video Adapter TVCS-183|http://cgi.ebay.com/New-Switchable-Apple-Mac-to-VGA-Video-Adapter-TVCS -183
W0QQitemZ6739937687QQcmdZViewItemQQptZPCA_Cables_Adapters?hash=item191bb4997&trksid=p3286.m20.l1116]
Connect it to the video port on the internal chassis. Connect the VGA cable that goes to the external display to the adapter. Just set the switch on the adapter to the side that says VGA, and it works. An interesting benefit is that, if your external display can handle higher resolutions, you can go as high as 1600x1200 (thousands of colors) using the iMac's built-in video (if it has the full 6mb VRAM). 1280x1024 at millions of colors. The best you can do with the built-in display is 1024x768. You can consider an
upgrade (instead of a broken iMac). 🙂