Server App and Admin not allowing me to connect

I am having nothing but troubles -- my name and password are correct and work for mail, but when trying to remote admin the machine on even the local network, neither application can connect to the server. It just says it cannot connect. I've tried rebooting and even made sure that the advice at the following article was followed, to no avail. It simply won't let me connect any longer. What else can I try?

http://support.apple.com/kb/TS3960

I know the name and password are correct because I can log into the machine directly with them, and I can still get my mail, I just can't admin the machine at all. Frustrations galore.

It gets worse

So not only is it rejecting my password to admin the machine from Server.app on a remote computer, it's rejecting my password for VPN. This is making me nuts -- how can it accept my password for some things and not others? (Screen sharing, for example, lets me in with my password, as does Mail).