the COUNT() function only excepts on parameter or * and the key word DISTINCT with that one parameter. The parameter is the column name. Your trying to use this function on more then on column and it does not allow more then one column as its param. Since your using this on one table just use
$totalResults = "SELECT COUNT(*) AS ['total'] FROM machine_problem_rhoda";
You can add conditionals to to see if something is not right like register date etc...
for example if you have registration you could get the number of people who joined this year
$totalResults = "SELECT COUNT(*) FROM machine_problem_rhoda WHERE YEAR(registration) <> '2011'";
If your using what I wrote as the config feel free to change it,add to it etc... That was simply a demo so you could get the overall idea of what needs to be done. I still recommend using the propel CRUD for this or maybe just using codeignitor framework for RAD(rapid application development) purposes.