Disclaimer: I am not a professional appliance technician. I have fixed my own appliances before, and many years ago, I used to sell appliance parts.
Please be careful when fooling with this; not only can 240 V kill you, it will hurt the whole time you are dying. Also, dryers tend to have sharp sheet metal edges in them; wear a long-sleeve shirt and maybe gloves.
Have there been any lightning storms or power outages in the area in the past couple of days? Sometimes the spikes and surges from those can fry things.
For "no heat", it could be one side of the 240 V to the dryer missing, a bad heating element, bad regular thermostat, bad high-limit switch, or bad control board. In some dryers, only the heater runs on 240 V, and everything else runs on 120 V; if you lose one leg of the 240 V, everything else but the heat will work. (In others, both the heater and motor run on 240 V and everything else is 120 V; the timer/controls might appear to work but nothing else will happen.) To check the 240 V, unplug the dryer and use a voltmeter on the outlet. If half is missing, look for a bad connection to the outlet, at the breaker panel, or maybe a bad breaker or fuse.
Usually, there will be a wiring diagram folded up inside the control panel or pasted inside the back of the dryer. Refer to this once you start fooling around inside the dryer.
A bad heating element is pretty easy to find with an ohmmeter; open circuit = bad. Also check from both ends of the heating element to ground (the metal chassis of the dryer), some elements can break apart and short to ground that way.
A "classic" dryer will have at least one regular thermostat, located somewhere in the air flow, that switches the heat off and on as the dryer runs. This usually looks like a little black cylinder, about 1/2"-3/4" diameter and 1/2" high, with a couple of tab terminals sticking out of it, and wires plugged on to the tabs. If this fails open all the time, you will get no heat.
If you have electronic controls, there is probably a much smaller temperature sensor (like a tiny bead of epoxy on the end of two tiny wires), and the control board turns the heat on and off, probably using a relay. The control board should be able to tell if the temperature sensor is unplugged or broken, so if you aren't getting any error codes on the display, the sensor is probably OK. Maybe the wire between the heater and relay fell off, or the relay is stuck open. You may or may not be able to get the relay by itself as a service part; you might have to replace the whole board.
Either a classic or modern dryer will have a "high limit" thermostat or thermal fuse. This is also located somewhere in the airflow, and has a temperature rating of maybe 30 or 50 degrees F above the highest temperature the dryer should ever generate. It only opens up if there is a bad problem (like the dryer vent is crushed, or full of socks or ice or a bird's nest) and the dryer overheats severely. It is a safety device that works independently of the regular thermostat. A high-limit thermostat will let the dryer run again once everything cools back down. A thermal fuse will never work again once it's "blown" - you have to replace it.
For the motor weirdness, it could be that the contacts on the motor relay on the control board are stuck together. That happens sometimes; the contacts arc a little every time they open or close, and eventually they get so pitted and beat up that sometimes they stick. Sometimes a motor on its way out will draw more current than usual and accelerate this process, but usually you can tell this, because the drum will be slower than usual, or it will refuse to start up with a big load of clothes.
I haven't been inside a new enough dryer to know whether this relay is a separate part with wires to it, or is soldered on to the control board. Either way, you can test it with a multimeter. If it's a separate part, you can buy one and try it, but if it's soldered to the control board, you might have to replace the whole board.
It's also possible that the relay is fine but that the control board has gone crazy and is always telling the relay to turn on. About all you can do for that is a new control board. Sometimes they go nuts due to voltage surges or old age. Sometimes a person or persons unknown spills the entire bottle of Downy on the control panel and it leaks inside the dryer and corrodes the board, which causes it to go nuts. This is easy to tell by looking. :)
There are a few sites online that will sell you appliance parts; you can look them up by model number. I usually look up parts on these to get a price, and then go down to my local appliance parts distributor. Their price often beats the online price by a little bit, plus I get to have it in my hands today. (That was with me paying retail over the counter at the distributor; appliance techs that do lots of business with the distributor get better pricing.) If you decide you need the control board, and it's real expensive to get an original part from Samsung, some distributors stock or can get rebuilt control boards for the more popular appliances, which can save you some money. Winchester may not be big enough to have a distributor, but there is probably more than one on the VA side of the DC metro.
Good luck!
