** I used a screwdriver to activate the switch and then the washer proceeded through the rest of the cycles as usual. The plastic piece on the bottom of the lid does not appear to be damaged. **

Than there may be a problem with the lid switch's mounting. The switch may be broken (even if still functional) preventing it from being activated.

** Could something be getting in the way? **

There's a slim chance but fairly unlikely IMO.

** What is the easiest way to get to the switch to check? **

There isn't actually an "easy" way but the procedure to access it is described at the following link. You can see the lid switch for your washer model at the second.

- Direct Drive Washer Lid Switch Replacement

LINK > www.the-appliance-clinic.com/ddlidsw.html

- Kenmore 110.24642300 Lid Switch

LINK > www.appliance411.com/data.php?rc=547222

JFYI

Dan O.

www.Appliance411.com/parts/?ref411=Kenmore+Washer

The Appliance Information Site

=D~~~~~~

thanks!