I want to use find (or something else) to give me a list of all files in a directory tree where the group access is not rwx or rw-. I'm trying to archive the whole directory tree, but it won't archive any files where I do not have at least read access. I have tried:
find . ! -perm -060 but that doesn't give me what I'm looking for.

"ls -lR | grep '^...---' and that does give me (more or less) what I want, but it doesn't give the full pathname for the files. There doesn't seem to be an option for ls that will print out the full pathname for me.

BAsically, I want to get a list of files so that I can go to the owners and get them to do a chmod. I would be much simpler if I had root privileges, but unfortunately I don't.

Any help would be appreciated.

the process you start has EUID of your account, if the permissions are not sufficient it normally has to be rejected. The backup software usually takes some nologin (pseudo) user that has backup sufficient permissions and you suppose to sudo to this account to perform backup. Such account normally called "backup operator". That is why we have security.

We don't have sudo capabilities. What we are told that we should do is send a request to our (external) unix management team to ask them to do the archive (and retrieval if we need something retrieved). However, I an't wait for 2-3 days to have the request actioned, so that is why I do it myself.
We are told that outsourcing our unix support is cheaper than having our own in-house support, but I'm sure that they didn't factor in the down-time and frustration level of the end-users.

No, they only factor in cost. Cost wins.

If you don't have regular backups then I hope you don't have any valuable data - could prove a lot more expensive than having proper support.
However, I don't see why your find command didn't give you what you were looking for - have I misunderstood?

cheers