That's an almost sure sign Java is invoked without the necessary
-jar parameter. Most likely Java does run, says it can't find the main class, and exits immediately. This happens so fast you only see the black box (a command line window) flash up. This problem isn't uncommon, but it usually isn't so difficult to solve.
As a workaround, you can
- in Windows Explorer, right-click in the folder where languagetool.jar is located,
- create an empty text file and open it,
java -jar languagetool.jar,
- save the file as e.g. LT.bat (without the .txt extension!),
- double-click LT.bat to start LanguageTool.