Mac Pro during start up, chimes, apple logo then shuts down. Just began

The chime is generated in software when your Mac passes the Power-On Self Test. If a suitable source of software can be found, booting is likely.

The dark gray Apple is not resident in any ROM. It can appear only after it is loaded from a boot device.

Your Mac will shut down during boot-up if the Boot Drive is so damaged that it cannot be mounted.

-------

So focus your energy on repairing your Boot Drive using Recovery_HD or the 10.6 DVD, as appropriate.

Safe Mode requires a Bootable drive, so not being able to invoke Safe Mode in this case is no surprise.

Hold down Alt/Option at Startup to invoke the Startup Manager. It will very slowly draw an Icon for each Bootable Volume. When it is done drawing, the Eject key goes "live" and can be used to open the DVD Reader to insert the Installer/Utilities DVD. It will eventually draw an Icon for that as well, but again, very slowly.

Try mouse down

Try Option key

direct connect kb to the front USB port and mouse to the other front USB port

then zap pram from cold boot - command option p r - while system does 3 reboots before you let go.

remove all the drives but the system drive too, just slide half way out.

PCIe cards can even interfere.