The plugin is bundled since TeamCity 5.0. See the usage details in the current documentation version.
You can get details on errors and REST request processing in
logs\teamcity-rest.log server log.
Please turn on debug logging (e.g. set Logging Preset to "debug-rest" on Administration/Diagnostics page or modify Log4J "jetbrains.buildServer.server.rest" category) to get details about each processed request.
If you need to extend the plugin with your functionality, you can base your plugin on the current REST API plugin code, but make sure that your plugin does not interfere with the bundled REST plugin. To achieve this, change the
teamcity-plugin.xml file to have a different plugin name and a different value for the "api.path" parameter. Once this is done, your patched plugin and the original REST api plugin can work in the single TeamCity installation.