Good Morning @paulh.t2x861,
My apologies for not responding sooner! Indeed, there is both an early and late 2009 iMac. Apple really needs a better naming convention but I digress.
Since Anywhere works on your Windows 7 PC while it’s connected to CenturyLink, that would seem to rule out something with Republic’s servers or your Internet connection. Therefore, it’s time to look further at the iMac. If you look at System Preferences -> Network -> Advanced -> Proxies; do you see anything interesting there? This is a shot in the dark but you might try adding the following string under “Bypass proxy settings for these Hosts & Domains”:
all.pro.mqtt.igate.nocell.io:443, s3-1.amazonaws.com:443, auth.republicwireless.com:443, clients.l.google.com:80, api.republicwireless.com:443, api-d.republicwireless.com:443, cognito-identity.us-east-1.amazonaws.com:443, mobileanalytics.us-east-1.amazonaws.com:443, sts.amazonaws.com:443
These are the domains one typically needs to whitelist for use on corporate networks. I realize you’re not on a corporate network, however, it’s worth a shot.
If that doesn’t work, you might try deleting the Anywhere preference files. You’ll find those at Users -> Your User Account -> Library -> Preferences -> com.republicwireless.anywhere.plist and com.republicwireless.anywhere.helper.plist. Before deleting those files, I suggest killing any running Anywhere processes using Activity Monitor. To do so, open Activity Monitor (it’s in the Utilities folder), search for Anywhere, then Force Quit any instances of both Republic Anywhere and Republic Anywhere Helper.
If neither of the above help, we’re pretty much out of non-destructive options. If necessary and you’re up for destructive (to Anywhere messages stored on the Mac not the Mac itself or to messages on your phone), let us know.