I'm not very good with solder wick, so I pulled out my trusty "solder sucker" and got the holes cleaned out. It's kind of brute force, but it worked.
On my 24" iMac, I only needed to disconnect the first LCD Cable (before removing the LCD's torx screws), then I was able to pivot the LCD up 90 degrees, to get access to the hard disk. It was nice not having to disconnect (and reconnect the 2nd and 3rd cables. Now I have 3TB! (Seagate Barrracuda ST3000DM001). Note: I first tried putting the 3TB disk into an SATA USB enclosure, so I could transfer the data before opening up the iMac, but I found out the some of the older USB enclosures don't work with >2TB disks.
My daughter's iPod Video "died" - didn't respond to charging, plugging into a computer, or resets. I had replaced the headphone jack/hold switch and battery a few months back. So I decided to open it up again. I tried disconnecting the battery and plugging in the old battery - the iPod came on! So I reconnected the newer battery, and tested it - everything seemed to work, so I closed her back up. It seems to be working fine. Maybe it just needed a "hardware reset" - e.g. disconnect and reconnect the battery.