I'm not sure what's the cause for that error (PHP or ADOdb), but a new version of ADOdb will fix the problem. I've attached a slightly modified version of ADOdb v3.30 that works with LinksSQL. The reason it's been modified is that ADOdb either lower()'s or upper()'s the column names in the results, and I've disabled that (the change is in adodb-recordset.inc.php). I've got this running on my machine here, so it should also work for you.
I forgot to mention, that you can just uncompress the attachment right into admin/Links/PHP (it uncompresses into the adodb directory), but you should move your current adodb to adodb.old before you do this.