Can you record a video of the problem? Doesn't sound like something I've ever encountered.

Be sure to unpack the zip and then start livesplit.exe and/or livesplit register.exe. If nothing happens try to open it as administator. Also it can be that it opens, but only as a small timer and can be hard to spot. You can try to open a set of splits instead of opening livesplit.exe.

You gotta extract it first. That's most likely the issue.