Greetings fine DIY-er! In the spirit of true at-home masterminds, let's tackle a noteworthy kitchen hiccup today. We're surely going to whip our engineering aprons on because fixing a rice cooker that won't shut off is on the menu. Remember, you're the chef of home repairs, fixing a digital conundrum is merely your recipe for the day!

Spot the Clues: Understanding Your Rice Cooker

Firstly, don your detective's cap, because it's essential to understand the basics behind our miniature kitchen marvel. A rice cooker works by using a thermostat to keep tabs on the temperature of the pot. When it reaches a certain heat level, indicating that the water has been wholly absorbed, it flips the switch to 'Warm'. The snag here could be that a rogue element is at large stopping this transition.

The Usual Suspects: What Could be At Fault

In identifying your rice cooker's issue, I've rounded up three usual suspects:

1) Faulty thermostat: An obstruction or non-functional rice cooker thermostat will keep your appliance at 'Cook' mode.

2) Damaged switch: A damaged or sticky switch, acting like a stubborn mule, refuses to be budged to 'Warm'.

3) Problematic circuit board: A defective circuit board can oversimplify the cooking and opt to sidestep the ‘Warm' refuge.

Don't worry, we're going to deal with them one by one.

Rice Cooker Repairs: A Step-by-Step Guide

Step 1: Safety First

Obviously, I don't want to lose you to a shocking experience, so remember to unplug your cooker before anything else!

Step 2: Undo the Mysteries

Open up your rice cooker and locate these three characters– the thermostat, switch, and circuit board. Experienced DIY detectives, this is your field of play!

Step 3: Interrogate the Thermostat

Investigate your thermostat for debris or disconnection. Cleaning it with a dry cloth or reconnecting any loose wires could solve the issue. If not, it might need replacement - cue the sobs.

Step 4: Cross-Examine the Switch

Sometimes a switch can be a mischief maker! Wiggle it around to see if it's stuck. In case it is, a swift clean can save the day. If it appears damaged, then alas, it's time for it to retire (read: replace!).

Step 5: Put the Circuit Board under the Lens

Lastly, our circuit board. If you spot any obvious signs of damage like burning, a replacement is unavoidable. However, if there are misbehaving wires simply not in the right place, a careful retouch can resurrect our beloved cooker.

Reassemble, Rejoice, and Rice!

Now, reassemble the parts carefully remembering to give each its deserving place. Give your cooker a test run (don’t forget to plug it back in!). If we did our job right, the relentless cooking should cease, and the cooker should finally relax at 'Warm'.

When It’s Time to Dial the Pros

Despite all the fun we’ve had dissecting and diagnosing our rice cooker, sometimes the problem might be beyond DIY rescue. If the above steps don’t fix your appliance, it could be a deeper issue that only the manufacturer or an appliance repair professional can tackle. There is no harm in handing over our DIY badge, even if for a day.

The Showstopper: When It’s Time To Say Goodbye

Finally, do consider the undeniable truth. In some cases, an aged appliance might have given all it had to give. Opting to replace your rice cooker can sometimes be the wiser (and more economic) choice.

Whatever the result, stand tall, for today you've donned the spirit of a true DIY repairer. By troubleshooting, experimenting, and perhaps even wearing the sweet grime of victory, you have triumphed. So, go on and give your rice cooker a knowing nod, cook that victorious meal and taste the richness of self-repair. Because no matter the end result – whether it's brand new, repaired, or merely understood – your journey in fixing a rice cooker that won’t stop packs in resilience, curiosity, and fun. Now isn’t that the real feast?