I re-ran the service installer to get the default lansweeperservice.exe.config file back.
Changed that password to match what I have the lssqluser32 password set as.
Now I get this in the errorlog.txt file:
12/2/2008 3:45:48 PM : Cannot connect to database, check your config file, service will be stopped
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Login failed for user 'lssqluser32'.
I've even gone in and reset the password in SQL manager to make sure it was correct.