I have a Kenmore 600 series I'm having problems getting the back of the dryer off. It seems to have spot welds holding the back on.

Generally take top off, then control panel then front.

Check your breaker by turning it off and back on. Then check wiring at plug and back of dryer. You could have a bad relay switch. You can find it under the top and put the 2wires together and try it then . If it works, you know that it is the relay switch. Last but not least, it may be your element. Check it visually to see if there is a break in it or a weak spot.

ALWAYS UNPLUG YOUR DRYER BEFORE STARTING ANY REPAIRS
Your problem sounds like drum rollers have flat spots on them .
If you have a front loading machine,

Remove the electrical console that holds the timer switch, start switch, etc. from the top of the dryer.Also remove the screws holding the lint filter in place.
Be REAL CAREFUL not to knock any of the wires off of the timer switch. Then remove the top of the dryer.
Remove the front of the dryer. This will expose the drum and belt. Remove the drum and belt and this will expose the drum rollers, idler arm pulley and motor.
Now is a good time to check the belt condition for wear.
Be sure to note the route of the belt, this will come in handy when you go to reinstall the belt.
Check your drum rollers for flat spots or wear, if they have flat spots or wear on them replace them.
If the drum rollers don't have flat spots or wear on them then they probably only need lubrication. Lubricate the shaft of the rollers with a good grade of machine oil such as 3 in One oil. Reassemble the dryer, plug back in. This should solve your noise problem.
I will include these two websites for parts and further help:
http://www.partselect.com/
http://www.appliancepartspros.com/index.aspx
Both also have chat assistance 24/7.
Good Luck,
I hope this helps
Please do not forget to rate me,
Thank You

can you hear the motor running, if so then more than likely the belt broke, you need to unplug it ,remove the front cover, then top cover, then remove drum and you can start to restring the new belt

UNPLUG YOUR DRYER BEFORE STARTING ANY REPAIRS
Your problem sounds like drum rollers have flat spots on them or in need of lubrication.
If you have a front loading machine,
Remove the electrical box that holds the timer switch, start switch, etc. from the top of the dryer. Be real careful not to knock any of the wires off of the timer switch. Then remove the top of the dryer.
Remove the front of the dryer. This will expose the drum and belt, remove the drum and belt and this will expose the drum rollers.
Check your rollers for flat spots, if they have flat spots on them replace them.
If they don't then they probably only need lubrication. Lubricate the shaft of the rollers with a good grade of machine oil such as 3 in One oil. Reassemble the dryer, plug back in. This should solve your noise problem.
I will include these two websites for parts and further help:
http://www.partselect.com/
http://www.appliancepartspros.com/index.aspx
Both also have chat assistance 24/7.
Good Luck,
I hope this helps

check you're thermostats for continuity, they are normally 3 thermostats, reset stats have a button on them please press, if not thermostat its your heating element

believe that model has lower front panel remove it ..clips each side top edge press them down pull panel off ..element ,fuses thermostat behind it

Go to YouTube and search for "Kenmore Dryer Repair" There is a guy that has posted over 22 "2 minute" video's on how to disassemble and troubleshoot dryer problems, he is fantastic and should be able to figure out what is wrong by watching his videos.

start outside at exhaust hoot look for blockage there first look for steep dip or drop in line where condensation can acumilate

Electric or gas?