OS X (Apple)

If it's your disc that came with your mac, then both the "c" and the "option" key should allow start it up from the disc, so something it wrong with either your drive or your disc. You can try this Resolve startup issues and perform disk maintenance with Disk Utility and fsck

As far as I remember "Cmd+V" is not for "safe-mode" boot but for "verbose-mode".

Try with "D" or "Cmd+D" to see that your drive does not have any issues (it should launch AHT utility).

As a totally different, cheap, passive, dirty and lazy approach you can take your mac to any apple store and I bet they'll help you boot and -if necessary- reinstall the OS for free.

if a pre existing file made by the developer had a sha 1 sum of that file in a database, that file could be checked for corruption.

just a thought that crossed my mind.
maybe some one could ask a OS developer what they think of every structural related file having a integrity check method and related value in a database.

What you're describing is similar to tripwire:
Open Source Tripwire® | Free System Administration software downloads at SourceForge.net

Also installable via MacPorts.

You could also try booting from a LiveCD e.g. Fedora, CentOS, Ubuntu if the Mac is an Intel version (you can also get PowerPC CDs for Yellow Dog Linux).

This will enable you to erase the hard drive in the Mac & re-install your OS. If you haven't another machine to download an iso, go to an InterWeb cafe & search Google for Linux CD vendors. They generally cost about £3 or £4 each.

---------- Post updated at 06:42 PM ---------- Previous update was at 06:34 PM ----------

also on having re-read your post, there is no Extensions Manager on OS X. That was only used on the Classic Mac OS from v.6 ==>v.9.2.2...

What was the name of the file you deleted (i.e. ~/Library... or /Library...)?

All current iMac models respond to the "c" key to request booting from the optical drive (make sure it is ONLY the "c" key, no shift, option, or command, or anything else). Automatically ejecting the disc usually means that it cannot read the disc at all. Check for scratches, and try a disc polishing/scratch removal system if you see anything heinous. It might also mean that your drive is having problems. There are a few other options, though, to get your system back up. You can hook up an external drive with an up to date version of the system software and boot from that by using the option key method mentioned earlier. This gives you the boot selector screen. The fact that your optical disc did not show up there either also indicates that either it cannot be read, or that it is not a valid boot device for your hardware. Are you sure it is the disc that came with the computer? Yet another method, if you have another Mac available, is to boot the iMac in "target disk mode" by holding down the "t" key at startup. This basically turns the iMac into a very expensive external hard drive. Then, you can hook it up to another Mac via firewire and install the system on to it from that Mac. There are some drawbacks to this method, but it will work well enough. After doing this, re-run the latest combo updater from support.apple.com.