You can't lose anything just by booting and if it isn't in the tray, it can't do anything!
You can hold "mouse down" during boot to cause the tray to slide open in order to pause and insert the CD/DVD at that point - you would then need to select it as the boot volume on the screen (Mac does have boot selector).
You did read what Grant said about what to do and how.
Resolve startup issues and perform disk maintenance with Disk Utility and fsck - http://docs.info.apple.com/article.html?artnum=106214
Using Disk Utility in Mac OS X 10.4.3 or later - http://docs.info.apple.com/article.html?artnum=302672
Disk Utility's Repair Disk Permissions 10.0-10.6 - http://docs.info.apple.com/article.html?artnum=25751
"Try Disk Utility" (modified from http://support.apple.com/kb/TS1417)
1. Insert the Mac OS X Install disc that came with your computer (Edit: Do not use this disc if it is not the same general version as what you have currently on your computer, e.g. use a Tiger disc for a Tiger drive, not a Panther disc), then restart the computer while holding the C key.
2. When your computer finishes starting up from the disc, choose Disk Utility from the Installer menu. (In Mac OS X 10.4 or later, you must select your language first.)
Important: Do not click Continue in the first screen of the Installer. If you do, you must restart from the disc again to access Disk Utility.
3. Click the First Aid tab.
4. Click the disclosure triangle to the left of the hard drive icon to display the names of your hard disk volumes and partitions.
5. Select your Mac OS X volume.
6. Click Repair. Disk Utility checks and repairs the disk."
Then boot in Safe Mode, (holding Shift key down at bootup; takes longer to boot this way so be patient), run Disk Utility in Applications>Utilities, then highlight your drive, click on Repair Permissions, reboot when it completes.
Mac OS X: Starting up in Safe Mode - http://docs.info.apple.com/article.html?artnum=107393
What is Safe Boot, Safe Mode? (Mac OS X) - http://support.apple.com/kb/HT1564
Safe Boot takes longer than normal startup - http://docs.info.apple.com/article.html?artnum=107394
Mac OS X 10.4, 10.5- Computer shuts down during Safe Boot - http://support.apple.com/kb/TA24054
If you don't have an installer disc available you can try effecting repairs using fsk in Single User Mode - http://docs.info.apple.com/article.html?artnum=106214.
Post by japamac about using fsk - http://discussions.apple.com/thread.jspa?threadID=1649143
Mac Running Slow: General Tips & Advice (Kappy)
https://discussions.apple.com/thread/4214422?