My comments will be suggesting that you post on several forums. I do have one request -- whenever you do find a solution please come back to this thread and post a description of what worked for you. Thanks.
1 - Your post here does not really say what you attempted to do in order to transfer your catalog from v8 on the old computer to v10 on the new computer. Did you do any copying of the v8 catalog to the new computer ? Did you copy your photo files from the old computer to the new computer ?
2 - Specifically
what command or what function were you attempting when you experienced the message -
"error encountered while writing file" ?
Perhaps the simplest answer would be to wonder if this could be some type of permission problem - however, more info about the function being attempted could help with this symptom. Also, what version of Windows, will the catalog be in the default location or if not where ? Where are the photo files ?
3 - One method that has a good success rate is to do a PSE backup on the old computer (this PSE Organizer Backup includes the catalog and the photo files) and then do a PSE Organizer Restore on the new computer. However since you say you don't have the old computer this approach can not be used UNLESS you have a PSE 8 Organizer Backup taken on the old computer.
4 - "So, can you download your backup catalog from the adobe site?"
IF YOU synched ALL your photos (and other media) to the photoshop.com site, then I think it may be possible to bring most information from photoshop.com back to your new computer and PSE 10. I have not done this process -- for assistance I would call Adobe Tech Support, mention that you just purchased PSE 10 and ask for upgrade assistance - OR - post this question on the Adobe site PSE forum.
5- Another forum which has significant activity about Photoshop Elements is Elements Village
http://www.elementsvillage.com/forums/index.phpIt has a subforum for versions 7/8/9 and that is where I would look and post. (don't worry that it does not include 10 in the subforum name)