In my case, it was that I didn’t edit and rename the wp-config-sample.php to make my new wp-config.php, simply copied the old one. Adding,/em> the extra lines (including that DB_CHARSET line) back in to the wp-config.php file was the thing that solved the weird character problem for me.
My weird characters were not the ? and a€ kind, though – I had little black diamonds with what looked like tiny white question marks in the middle! Anyway, using the correct wp-config.php fixed it right up.
Hope this helps someone…