Mac Pro 2x3 GHz Dual Xeon, 4 GB 667 MHz memory, OS 10.7.5, Aperture 3.4.3. Library (124 GB) is on an external drive WD 2T. Backup is on another external drive WD 4T Raid 1. Both drives have at least 500 GB free. Not seeing anything in Activities like "Processing" or "Writing to Drive" or "Waiting" or "Zzzzzzzz". Current file size is 7 MB from camera, not using raw images... most images are smaller. The 65 GB free is on the internal system drive. 20,000 images in library.
Mike, do you have a flip-camera or perian installed? Then you may have the 3ivx plug-in installed and that can make Aperture unresponsive. In that case remove the 3ivx-codec, see this support article:
Also a curruption of the Aperture library may be causing this, so try if repairing or rebuilding the library will help, see: Repairing and Rebuilding Your Aperture Library: Aperture 3 User Manual
Hard drives slow as they fill so make sure the main drive stays less than an arbitrary 70% full.
My expectation is that you have inadequate RAM in that relatively old box for most Aperture workflows, but IMO each of us should empirically evaluate whether or not we have adequate RAM:
Look at the Page Outs number under System Memory on the Activity Monitor app before starting a typical long Aperture work session and write the number down. Recheck the Page Outs count after working and write the number down again. If the page outs change (manual calculation of ending page outs number minus starting page outs number) is not zero your workflow is RAM-starved. Ignore the pie charts and other info in Activity Monitor.
If your test and calculation showed that page outs increased at all during operation you can
• add RAM (very strongly recommended).
Personally IMO increasing RAM to 8-16 GB from OWC http://eshop.macsales.com/ or from Crucial is a no-brainer at today's prices. I found my 2011 MBP ran Aperture alone fine under 8 GB RAM but Aperture + concurrent Photoshop would page out, so I upgraded to 16 GB RAM.
• and/or simply try to run Aperture by itself, especially no browsers open
• Restart before Aperture work sessions to clear possible memory leaks
• and/or switch from 64-bit operation to 32-bit operation (which will make some additional RAM space available). I do not recommend this, but see Switching Kernels: