Well, the first step in troubleshooting is to make sure the computer is plugged in and is getting power.

The basics: is Java working? Haven uses Java Web Start, so make sure "Java in browser" is enabled. Make sure that the cache for Java is turned on. (All of these produce very specific errors, though, so I doubt any of these are the issue.)
If an error is generated without being displayed, there should be something like "hs_err_pid.log" somewhere on your computer, likely in the Java folders if I recall right (default location for these files is the Java working directory, but can be manually set by a developer). A search will find it.
It's hard to say what the problem is without that log, so if you could post it, it'll help troubleshoot.
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