That means there's either a serious problem with the iBook or the iMac that's causing the problem. You said the iBook is on its last legs, so if there's a problem with the hard drive then you will have a problem.
If you are able to see the iBook on your iMac's Desktop, then you might consider transferring data manually rather than using MA.
You should consider repairing the hard drive and permissions on both computers:
Repairing the Hard Drive and Permissions
Boot from your OS X Installer disc. After the installer loads select your language and click on the Continue button. When the menu bar appears select Disk Utility from the Installer menu (Utilities menu for Tiger, Leopard or Snow Leopard.) After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list. In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive. If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the installer. Now restart normally.
If DU reports errors it cannot fix, then you will need Disk Warrior and/or Tech Tool Pro to repair the drive. If you don't have either of them or if neither of them can fix the drive, then you will need to reformat the drive and reinstall OS X.
