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Replacement parts for WHIRLPOOL LER5620KQ1 | AppliancePartsPros.com

Here is a wiring diagram
http://www.servicematters.com/docs/wiring/Wiring%20Sheet%20-%208528187.pdf

Sounds like you are not getting 240 volts to the unit.
The reason I say this is that on this unit in timed dry the timer runs off the 240 volts directly (TM/WB timer contacts closed). You said you tried all modes and it will not advance or heat and both of theses require the 240 volts.

Try flipping the breaker off/on slowly a couple times, sonetimes you can loose half the line without actually tripping the breaker.

Do you think I should replace the timer?
No, I would invest in a meter or get a friend to check it for you.
Just putting parts into a unit without some further troubleshooting will just cost you money.
Also on the timer the heater contacts in the timer and the timer motor would have to have gone bad at the same time and this is unlikely.

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.
Be careful as 240 volts is lethal !!!

Once you confirm that the unit is getting the correct power using AC volts scale, you can use the meter to find the faulty part using ohms (unit unplugged) which is much safer that trying to locate a bad part with power on.

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.