Does the remote host have to ability to ping the nagios server? If not, can the remote host run nsca and some plugins and deposit those results in some folder such as an ftp site? Surely they could do that. This result of the active service check could then be grabbed by the central nagios server through a cronjob that ftp's to the site, gets the file, and stuffs it in the var/rw/nagios.cmd file.
You said the remote application emails error logs to you. So just use "check_log" nagios check plugin to look at this log for the events you are interested in.