I've moved your post to the Backup and Restore topic folder.
First of all, are you using Centralized Backup in OneCare? Is the external drive attached to a computer in your Circle that is the Hub? If so, perhaps the problem is that the location has changed due to the new router, though this should not be the case since the location of the drive is still the same from a PC name perpsective.
Or, are you backing up both PCs to a NAT device? That is, the drive you refer to as external is a Network based unit with shared storage. If that is the case, then OneCare backup simply needs the permissions to be set correctly on the NAS for the location you are trying to save to. However, you are reporting that you are encountering a network error when trying to save the plan settings in OneCare, not when actually selecting the location or doing a backup.
Unless you are using Centralized Backup and the drive is external on the Hub PC, I would suggest trying to reset the backup plan on the laptop -
Open OneCare
Click Change Settings
backup tab
Click Configure Backup
Click change settings in the lower left
Make sure that the first screen for Centralized Backup has "No Centralized backup" selected
Click your PC on the left.
Uncheck the selection for "Turn on backup for this PC."
Click Next and save the revised plan.
Go back to the backup tab, configure backup and click Change Settings in the lower left once again.
Select your PC and click.
Click Turn on backup
Select the change location link and select the drive you want to use for backup
Modify the schedule as desired for "When"
Select the file types as desired for "What"
Click next and save the revised plan with the new selection.
If you are using Centralized Backup, try configuring the plan from the main PC and not on the laptop. Also make sure that the laptop and desktop firewall settings are allowing file and printer sharing for both options in the advanced ports/protocols list when connected to your Home network. it is possible that with the new router, your laptop wireless is on a different subnet now, causing the issue.
You can also contact support for help:
How to reach support (FAQ) - http://social.microsoft.com/Forums/en-US/onecareinstallandactivate/thread/30400b52-7f26-4ba0-bc18-17e305329d90
-steve
Microsoft MVP Windows Live / Windows Live OneCare Forum Moderator