Using a regular expression to validate whether input has any non digits in it

Simply:

function validInteger(theNumber){    
    return theNumber.match(/^\d+$/) && parseInt(theNumber) > 0;
}

Live DEMO

Or even simpler with regex only as suggested by @Eric:

return /^[0-9]\d*$/.test(theNumber);

Live DEMO

Update:

An excellent cheat sheet. The link died after 5 years, sorry.