Hmmm ... judging from the errors show appears to be Windows. And did you obscure the URL http://myltiprovider/? Is a Windows type shortcut URL and the other systems/browsers on different networks might have some issues with that.
And ... 'some random characters and a empty string' ... when I setup an LTI provider thang, there is a shared key generated. Maybe that's the issue ... in the first posting ... ie one of those 'invalid signatures' the 'random characters' you created?
It wouldn't hurt to check the plugins out to see if there is an updated version of LTI Provider.
Current version: 2.2 (2011121706)
for Moodle 2.0, 2.1, 2.2, 2.3, 2.4
'spirit of sharing', Ken