I cannot find any info on the given model number.
If this was bought from Sears then you are probably missing the first 3 digits.

Sears/Kenmore model numbers are usually 3 digits, a period and then and additional 6 to 8 digits.

[COLOR="Blue"]Can I assume the start button has gone faulty and needs to be replaced?[/COLOR]
No.

Here are your parts
Parts for Kenmore Dryer 11066712694 - AppliancePartsPros.com

The most likely culprit is the thermal fuse. This is mountedon the blower housing.
it is the third item on the first row in the parts.
If you go to the Sears parts site they have actual parts breakdowns.
Unfortunately they do not like to share theses with other vendors.

Unplug the unit and check the fuse with a meter should be 0 ohms.

Jiggery Pokery method is.
Unplug the unit.
Remove both wires from the fuse, short them together and tape them up so they will not short to the frame.
Plug the unit in and give it a try.

If blown, replace the fuse ASAP as it is a critical safety device re: prevents lint fires which can turn into house fires.

Also clean/check your vent system and the blower as these are the most common causes of it blowing.