Both my backup drives show up, but fail to boot, staying in grey screen with spin wheel.

I did some maintenance, copying lots of files, running Cocktail for the first time (failing to note exactly what I did) and after running Disk Warrior on both my bootable external drives (one OWC, one LaCie) they both hang in grey Apple screen with spinny wheel and never boot up, though both did earlier in the day, and have never failed to boot in years of service. Both appear on the desktop, show vertified in Disk Utility and booted up fine one day before all the maintenance. I don't know what Cocktail may have done, but it may have created a (now solved) problem for Photoshop 7, which crashed thereafter while loading, something that's only ever happened twice in six years. I managed to track down a TWAIN plug-in that had always been in Photoshop, something to do with scanning, but was now causing the crash. Anyhow, Photoshop is now working again, (after just removing that plug-in) but neither backup will boot up. Please don't suggest a system archive and install. I'm hoping for some miracle little file that once removed will restore the booting of the two externals. Your help is greatly appreciated. Please assume I am brain damaged and spell things out for the simple-minded. Thanks in advance.

I hope BDAqua sees this.

I only have one iBook, and it's less than half full; couldn't figure how to edit below that I'm now on 10.4.11. See what I mean?