On the advice of an online chat on this site, I replaced the thermal cut-off in my dryer. It is still not heating. I SPECIFICALLY asked if it could be the thermal fuse as well and if I should order one and I was told no, it was the cut-off, so I bought it. That did not help. What is the difference in the cut-off and the fuse? And why was I persuaded not to get the fuse if that could have been the issue? (and the cheaper fix)

I'm very frustrated as I go off to the laundromat instead of being able to use my dryer like I thought I would.

I am not quite sure how the diagram is supposed to help me. Simply, I replaced the cut-off per the advice on your site chat, not forum. I told them the dryer was running but not getting hot or drying my clothes. I told them at some point the vent hose had detached. (from the dry to outside) I was told to get the cut-off kit which I did and replaced the parts. It still does not heat or dry clothes. My question is, should I now replace the thermal fuse? Could that be the remaining issue?

OK the thermal cutout and hi-limit thermostats would be a reasonable part to replace giving your problem with the vent.

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

The first thing I would do is check the power to the unit. The heating coil requires the full 240 volts.
The meter should be set to an AC voltage scale higher than 240 usually this is 750 AC.
Try flipping the breaker off/on slowly a couple times. Sometimes you can loose half the line without actually tripping the breaker.
Check the voltage at the wall receptacle
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.
Do this with the heater off and on.
[COLOR="Red"]Be careful as 240 volts is lethal !!![/COLOR]

There is one diagnostic that can tell you if you have 240 volts without measuring it.
If the timer advances in a auto mode then you have 240 volts.
Note that if it does not advance this does not tell you that the 240 is bad as there are other things that could cause it to not advance.

If 240 is OK.
Unplug the unit and both wires from the heating coil.
Measure the coil should be around 8 to 12 ohms.
If infinite ohms replace the heating coil.
Also check from each side of the coil to it's case. Both should be infinite ohms. If not the heater is grounded and should be replaced.

If the heater is OK.
Measure across the hi-limit thermostat, should be 0 ohms.
Measure across the thermal cut-out, should be 0 ohms.
Measure across the operating thermostat (red wires), should be 0 ohms
With the uit still unplugged set the timer to a heat timed dry cycle and measure across Timer Switch 2 at the timer, should be 0 ohms.

With a little luck you will find the problem.
if not the you will have to do more troubleshooting.