How do I tell my version of libwww-perl?

Check the version of the module LWP

$ perl -MLWP -e 'print "$LWP::VERSION\n"'
5.805
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and, just to be sure, also check HTML::Form (part of the bundle), as I suspect the problem could have originated in that module (Update: this doesn't make much sense, though — as the revision control timestamp of the respective file dates back to 2005/12/07 :).  Mine shows 1.0.54.

I wonder what I am doing different from you.

No idea :)  Here's what I did:

use WWW::Mechanize;
my $mech = WWW::Mechanize->new();

my $url = "file:///.../test.html";   # the mentioned form
$mech->get($url);
$mech->current_form->dump();
$mech->set_fields( '__EVENTTARGET' => 'mynewvalue' );
$mech->current_form->dump();
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which gives:

$ ./674272.pl
POST .../Browse.aspx?MyToken=632797078501515540 [aspnetForm]
  __EVENTTARGET=                 (hidden readonly)
  __EVENTARGUMENT=               (hidden readonly)
  __VIEWSTATE=/wEPDwUJ           (hidden readonly)
POST .../Browse.aspx?MyToken=632797078501515540 [aspnetForm]
  __EVENTTARGET=mynewvalue       (hidden readonly)
  __EVENTARGUMENT=               (hidden readonly)
  __VIEWSTATE=/wEPDwUJ           (hidden readonly)
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