You'll know it's viable if the starter results in more yeast. When you first add wort to yeast for a starter, the wort will be a sort of translucent brown color. Over the next 24 to 36 hours, it will turn a creamy brown color. The color change tells you that the yeast have reproduced. Also, you will likely see some krausen form, could be a little, could be a lot, just depends on the yeast. This tells you that the yeast are actively reproducing.
You may not even need a starter, but I'd probably make one since the slurry is a month old. Use mrmalty.com (repitching from slurry tab - default settings should be fine) to figure out how much slurry you need for your batch based on the harvest date of your slurry. The result will be the amount of slurry (in ml, which you can convert to oz) that you need to ferment your batch. If it's more than you have, you can make a starter with a portion of the slurry.