Too many MySQL connections, Piwik not loading

We’ve had Piwik 1.8.2 installed on our server for several months, and all of a sudden we’ve been hit with this error message every time we try to load the site:

This just started happening this morning. The only way I can fix the problem is by restarting MySQL, but that only solves the problem for a little while, then it comes back.

Yesterday we had issues with user passwords being reset, and this morning I tried to log in only to find my user account had been deleted entirely. (There are only three of us with the admin pw, so it’s unlikely someone deleted it by “accident.”)

Unfortunately we’re running on Windows 2K3 server with IIS, so the error logs are essentially useless.

Edited to add: I updated to 1.8.4 on a whim, and that did nothing to fix the problem. When I’m finally able to log in, I get the following error messages in every widget:
Notice: Constant PIWIK_DOCUMENT_ROOT already defined in D:\LCTSites\WebRoot\piwik\index.php on line 12

Fatal error: Cannot redeclare _json_encode() (previously declared in D:\LCTSites\WebRoot\piwik\libs\upgradephp\upgrade.php:109) in D:\LCTSites\WebRoot\piwik\libs\upgradephp\upgrade.php on line 177

Additionally, looking at the MySQL Admin window, there are about 40 active connection threads. At some point it’ll overload and kill the whole application.