It will probably depend on your MSBuild/MSTest settings, especially for a gated build (which might do all kinds of things differently), but hopefully something in the following may at least offer you some clues...
The test results are usually dropped into the server's build folder (not the drop folder, but in the working folder in which the MSBuild process stores and builds all your source code, etc), using datestamped filenames for each of the test runs you have executed.
However it sounds like your folder is empty, which indicates that either you are looking in the wrong place (If you're doing a gated build, it may be that it uses a different working folder than a regular build, possibly alongside the C:\Builds\4 folder), or test results are not being generated (disabled or failing).
I'd try to find the build log as it'll almost certainly tell you what happened to the tests and if/where any results were written.
If you can locate the test results files, then you can usually just double click the main test results file to load the test results into Visual Studio (for display in the test results user interface) - so programatically you should be able to just Process.Start(testResultsFilename)
to launch Visual Studio to view the results (as long as VS is installed on the computer you're using your tool on).