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Replacement parts for MED5800TW0 models | AppliancePartsPros.com

Did you check the heating element with meter or see that it was broken before replacing it?
OR
Did you assume it to be the most likely cause and so re[placed it?

[COLOR="Blue"]Is there something that controls te electricity to the element that can be replaced[/COLOR]
Yes; there are a number of things.
Main thermostat (Item 8 in Section 3)
Thermal cut-off (fuse) (Item 9 in Section 3). Note: it includes a hi-limit thermostat. The hi-limit should have regulated the temperature so the thermal cut-off did not blow so it is assumed that it also did not function correctly. If you had a grounded element then the thermostat could not regulate the temperature and that is why the thermal cut-off blew.

There are other things but the above are the most common.

Try flipping the breaker off/on slowly a couple times, sometimes you can loose half the line without actually tripping the breaker and the heater requires the full 240 volts.
If this does nothing, check the voltage at the plug
L1 to L2 should be 240 volts
L1 to Neutral and L2 to Neutral, both should be 120 volts.
If OK
Unplug the unit and check the wires at the terminal strip in the machine to make sure none are loose or burned out
If OK
Check the power at the terminal strip.
[COLOR="Red"]Be very careful as 240 volts is lethal!!![/COLOR]

If you do not own a meter, I would suggest you purchase a one. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.

There is a good STICKY at the start of this forum about it's use.