It may be helpful to know if the drive is FireWire or USB? If FireWire, is it FireWire 800 or 400? Is the drive the type that uses the port for power, or does it have its own power supply? Was the drive partitioned and formatted with your old Mac, or was it erased (reformatted) when you started using it with the new iMac? Is if formatted for Mac OS X, or is it possibly formatted for Windows? The Mac format is called +Mac OS Extended (Journaled)+.
Also, regarding your new iMac, is it one of the current
new iMac models. Or, since your profile says iMac G5 and you are posting in the iMac G5 category (not the Intel-based iMac category), is it an older model that is "new" to you? I'll assume it is an Intel (not G5 PowerPC) iMac for the rest of this post...
This Apple article has information regarding +Error Code -36+.
http://support.apple.com/kb/HT2433
If this drive only has files that are backups of files that exist in your primary storage drive, you may want to erase the drive and re-copy the files over for the backup.
If you decide to do so, I would do it as follows to test the drive in the process. Run Disk Utility. Select this external drive in the sidebar. Be sure to select the DRIVE and not the volume indented under the drive.
If you want to see if there is data corruption on the drive currently, you can go to the +First Aid+ tab and run +Repair Disk+. If an error is reported and repaired, you can try using the drive again to see if the +Error Code -36+ problem still recurs. If not, you may have resolved the problem.
(Note: The next part will obviously erase whatever is currently on the drive.)
Otherwise, go to the
Erase tab with that external drive selected in the sidebar. Click on +Security Options+, and select the option to +Zero Out Data+. This will write zeros to all drive sectors as part of the erase process, so it serves as a stress test. If the drive is having problems or becoming unreliable, it will stall or error out. Depending on the capacity of the external drive, this process can take several hours to complete, but the progress bar should should show steady progress. If it completes in a reasonable time, the drive is probably fine physically.
To confirm that it is now set up optimally for use with an Intel Mac, select the drive in the Disk Utility sidebar and look at the bottom of the window. For +Partition Map Scheme+, it should say +GUID Partition Table+. Then, click on the volume (under the drive in sidebar). For
Format, it should say +Mac OS Extended (Journaled)+.
Use Finder to re-copy all the files you want to back up from your primary storage to this external drive. Hopefully, this error does not happen anymore.