A family of Microsoft word processing software products for creating web, email, and print documents.
I'm always dubious of "conversion" programs and I don't know anything about Pages so take this for what it might be worth ... nothing! :-)
Can you copy a table from a Pages document and paste it into a Word document and then edit the table. If you can do that then I would go back to the original Pages document and select everything and Copy/Paste it into a Word document.
You might also just try a test with that one particular table that's causing the problem. Maybe it's corrupted in the Pages document and thus if everything else came over fine, just recreate that one table.
Though you said you can't select it, Hmmmm...
Make sure your non-printing characters (backwards P on your toolbar) is toggled on and see if you can spot anything odd. Also switch from Print Layout View to Draft View to see if there's something you can see.
Hope something here helps