Mann jess
You say,
"I'm using J2SE 5.0 Update 10, with either Limewire 5.12.6 or 5.13 beta"
Ive never herd of L/W versions like this can you confirm.
Un install all java and all L/W versions COMPLETLY before reinstall of boath.
Oh & use the off line installer, for java.
Do a search on your com for L/W files and delete all of them
Oh coppy your D/L files to a new folder before deleting L/W.
Peace.

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mickjapa108