Downloading the current server software off mojang's website and launching it (minecraft_server.1.7.10.exe) causes it to crash on launch. Downloading a redundant copy, updating java, running with compatibility modes and running as administrator do not solve the issue.
UPDATE: There is no crash report or server log, or even a single error message. The program doesn't even get that far. Double clicking the application opens a new window which closes immediately. The server software does not even begin to run in the first place, ergo the absence of a server log.
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There is no crash report or server log, or even a single error message. The program doesn't even get that far. Double clicking the application opens a new window which closes immediately. The server software does not even begin to run in the first place, ergo the absence of a server log.

Use the JAR instead of the EXE.

Running the JAR file results in the same exact symptoms as the .exe, unfortunately. There is seemingly no difference in behavior between the two.

For technical support please use the Mojang Support Center.
Incomplete without crash report or server.log