If I go to the DEP/ARR page and select an approach without first selecting a STAR, it loads up what appears to be the waypoints for the first available STAR at the airport, and none of the ILS waypoints.  Subsequent attempts to load the ILS approach don't result in getting the approach into the FMC.

As an example, I tried to load the ILS 19C going into KIAD, and the waypoints that loaded were KASDY BARIN STAYO TRING, which are waypoints of the CAVLR3 arrival (the first alphabetically listed arrival for KIAD).

Bob

You have to choose first the Approach, then the STAR, then the STAR TRANS and at last the Approach TRANS.

For you, that should look something like this:
Approach ILS 19C
STAR CAVLR3
STAR TRANS DOORN or THHMD or TRSSK (with left LSK)
Approach TRANS (usually the different IAF for this approach) with right LSK

You can do an ILS approach without selecting a STAR.
When you go to the DEP/ARR > ARR, select a runway (no RNAV/ILS/VOR, i.e. 05, 12, 23, 30 (from YPAD)), it must be an ILS runway, from the list of runways at the bottom of the page. You can tell if they are ILS runways as you scroll through the list (i.e. ILS23-Y (again from YPAD)), before you get to just the runways. In this case, my selection is runway 23.
After doing that, if you look in the APPROACH REF page, you will see the ILS freq/hdg listed, and you a good to go (make sure there are no discontinuances in your route though).

Markoz wrote on Feb 13^th, 2019 at 1:34am:

You can do an ILS approach without selecting a STAR. When you go to the DEP/ARR > ARR, select a runway (no RNAV/ILS/VOR, i.e. 05, 12, 23, 30 (from YPAD)), it must be an ILS runway, from the list of runways at the bottom of the page. You can tell if they are ILS runways as you scroll through the list (i.e. ILS23-Y (again from YPAD)), before you get to just the runways. In this case, my selection is runway 23. After doing that, if you look in the APPROACH REF page, you will see the ILS freq/hdg listed, and you a good to go (make sure there are no discontinuances in your route though).

Exactly the way I do it, and have never had an issue. ;D

He can fly the ILS Approach without FMC, but that was not the question  ;)