By far the most common solution to this is to use one of the HTML modules. Yes, you say that the html is "non-standard" -- but, truth to be told, most HTML out there is, and the HTML-parsing modules know that, and are perfectly able to cope. If they were only able to deal with perfectly syntactic HTML, they'd be called XML-parsing, not HTML-parsing. :)
My personal favorite tool for extracting data from web pages is HTML::TreeBuilder -- in your case, it would be a simple matter of asking for all <td> elements, and grabbing the various answers out of them. You may find the dump method particularly useful in examining what the parser makes of your HTML.
perl -pe '"I lo*`+$^X$\"$]!$/"=~m%(.*)%s;$_=$1;y^`+*^e v^#$&V"+@( NO CARRIER'
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