I came across this question in an attempt to find a way to evaluate part of a function like it is possible in Excel.
Here is my dirty workaround - instead of outputting the result in an msgbox, you could simply store the value or displayvalue of the activecell in a variable and use it to your liking.
Notice however, that the function will temporarily overwrite whatever you have in your currently selected cell and it will need to recalculate the sheet before the result is available. Hence it's not a viable solution if you need to evaluate multiple cell values.
function evalPart() {
var ui = SpreadsheetApp.getUi();
myPart = Browser.inputBox("Enter formula part:", ui.ButtonSet.OK_CANCEL);
if (myPart != "cancel") {
myActiveCell = SpreadsheetApp.getActiveSpreadsheet().getActiveCell();
myBackup = myActiveCell.getFormula();
myActiveCell.setFormula(myPart);
Browser.msgBox("Result of \\n \\n" + myPart + " \\n \\n " + myActiveCell.getDisplayValue());
myActiveCell.setFormula(myBackup);
}
}