apple support can't seem to help - can you?

Sounds like you have some type of hardware problem. That could be the hard drive in your system is starting to fail.

With your newest external drive do a install of lion on that drive then boot the system from it and check to see if you have any problems running the system from that external. If you can pair the keyboard and create a time machine backup from it then that is a sign the internal drive is failing.

If after the install on a external drive you still have these problem then that points to some other hardware in the system. It could be the ram or the logic board is starting to fail.

An attempt to Repair Home Permissions and ACL's through the Lion Recovery thing - it ran for 4 hours to no conclusion.

This is a problem.

Boot your Mac normally and launch Console - it is in your Utilities folder. From the View menu, select Show Log List if it is not already shown. Select system.log from the log list.

In the filter field at the upper left type mdworker. You will probably find many errors associated with Spotlight indexing. Copy a couple dozen of those entries and post them in a reply. Do the same for mds.

Time Machine will not function until Spotlight builds an index and it sounds as though it never finishes. You can force it to reindex by performing the following:

1. From the Apple () menu, choose System Preferences.
2. Click Spotlight.
3. Click the Privacy tab.
4. Drag a folder or an entire volume (your hard drive) to the list.
5. If prompted for confirmation, click OK.
6. Remove the item or volume you just added to the list by clicking it and then clicking the minus ("-") button.
7. Close Spotlight preferences.

Spotlight will re-index the contents of the folder or volume.

This is unlikely to help given the failed attempt to repair home permissions and ACLs though. The reason for that is a mystery. Boot OS X Recovery again, select the startup volume, and click the Repair Disk button. Reply with any errors that it reports in red.

Whatever problem is causing this may best be solved by erasing your startup disk, followed by installing OS X from the Recovery partition, followed by observing the system's behaviour prior to installing anything more, followed by correlating Spotlight indexing subsequent to installing additional software. I realize you performed a "clean reinstall" but the definition of that is subject to interpretation.

1. Try temporarily excluding all external drives and backups including Time Machine from the Spotlight search.

Go to: Apple > System Preferences > Spotlight > Privacy and add all External Hard Drives including Time Machine to the "Prevent Spotlight from searching these locations" list.

Example:

Now see if Spotlight will finish.

2. Then if you have other external hard drives connected to your Mac, go to: Apple > System Preferences > Time Machine > click on Options and add all the external hard drive(s) to the "Exclude these items from backups" list.

Example:

Now see if Time Machine will properly complete a backup of your Macintosh HD.

If you still have AppleCare, schedule and appointment once again and have them deal with straightening out your issues instead of you. Let them service this iMac and solve and repair your issues. NOT YOU!

This is why you still have AppleCare in the first place. Give your iMac to Apple and let them deal with your issue.

Just make sure you have a backup of all of your data before bringing your iMac in for service.

With the consideration that your iMac's internal hard drive may be failing, if the hard drive in your iMac is a 1 TB Seagate internal drive, your 2009 iMac might be eligible for the free Apple Seagate 1 TB hard drive replacement program.

You can see if your iMac is eligible by inputting your iMac's serial number here.

http://www.apple.com/support/imac-harddrive/

If your iMac is eligible for the replacement, you can make an appointment with Apple or an Apple authorized repair center to do the hard drive replacement.

Also, if your iMac is close to the end of its 3-year extended AppleCare plan, my advice ( this is what I did I with my 2009 iMac) is have the Apple techs do a complete diagnosis of your system to see if it detects any other hardware or component failures in the event it finds a failure or near failure that can still be repaired and replaced under AppleCare. Also, you have them clean out all of the dirt, dust and debris that has accumulated inside your iMac at the same time.

Good Luck!

If you did a clean fresh install of os x on a erased hard drive there should be no reason or need to repair anything especially the permissions. I think you are being run around in circles. You need to do a clean install on a external drive and run the system from that. If the system runs fine from that external then you have a hard drive problem.

If the system does not run correctly from the external then you have some other internal hardware problem.

Agree.

If both the external and internal drives have been erased and a clean install done, the OP should not be having all of these issues.

There maybe another issue. Perhaps the internal hard drive replacement is bad. Can happen.