The reason the DVD is being pushed out at startup is because the system cannot find a valid System on the DVD.
Take the Apple Hardware Test Disk, that came with your machine, and attempt to boot from it. (follow the instructions)
If the machine boots from that CD, then the drive is working correctly. If it doesn't you may have a faulty DVD for Tiger.
Holding down the "C" should force the machine to LOOK at the Optical drive to see if there is a valid system in there, if there isn't, it will look in other locations, Network, HD, for one. Once it finds one, it will boot from it. Holding down the Mouse Button will EJECT the CD/DVD so that is a pointless exercise anyway. You could try Zapping the PRAM. Turn the machine on and immediately hold down the Apple key + Option + P + R until you hear at least 3 chimes. Then let go. Resetting the PRAM (Parameter RAM) sometimes sorts out a lot of things, including the Startup disk. You may have to reset date and time but that is a small point.
Do NOT try pushing the DVD back into the slot when the machine is pushing it out. You WILL loose. Do NOT try any hardware "repairs", you will loose again, this time it will be the warranty that you loose.
Let us know
I own a Mac Mini (1.42GHz, 80GB, 512MB, Combo, No AIrport/Bluetooth). It came pre-installed with OS X Panther and a DVD upgrade kit was included for Mac OS X Tiger. So after some use I decided o upgrade to Tiger. As per instructions i inserted the DVD, double-clicked the installer file which prompted me to click the restart button. The machine restarted fine, but at the time it was suppoed to boot from that DVD, it just ejected it without any reason, apparantly. Followed by a flashing Mac/ Question mark sign on a grey background. This followed by athe regular Apple logo and the machine booted up perfectly into its native OS. I tried a hundred times and the same thing happened. Then I thought it must have beem problem with the DVD like the drive being unsble to read the zero-track etc etc so I tried to factory restore the system with its bundled Mac OS X Panther Install DVD. Upon restart, this DVD was also ejected. Although, if I just force the DVD inside the slot loading combo drive just after it is being ejected, it then works ok but this is not the way it should be. I also tried holding down the C key or the mouse button (as instructed by Apple) by no luck. I checked the drive for any hardware defect but it seems tootherwise work, work and work....perfectly. I also changed the startup disk to DVD drive but no luck. Everytime the drive just throws out the media. Please help. The local apple support has no answer to this.