The cause of your thin lawn is not because you only mow once a week. Its
thin because it may lack one or all of the following
1) Nitrogen
2) water
3) sun
Your plan to core areate sounds fine and compacted soil may also be a cause
of your thin lawn.

Yes, compact soil may have something to do with the thin lawn. The
areas where the lawn thins the most are more or less the same areas
where I pile up the snow (near the driveway, near the walkway, and
near the curb). I really don't know for sure. Areating the soil should
help this problem if this is the cause of the problem.

Lack of water may also have something to do with the thin lawn. The
front yard and side yard only have a thin layer of top soil over sandy
soil. Therefore, they don't hold water that well. Top dressing the
lawn should help this problem if this is the cause of the problem.

By areating the soil and top dressing, I think I can get all the bases
covered.

I would areate, overseed and top dress with compost. You don't need to
rough up the soil before seeding because the areating will create lots of
soil contact areas. I would not use started fertilizer since you are really
just overseeding and not starting a lawn from sctratch.

I understand your suggestion of skipping the step in roughing up the
soil surface. This is great! This means I can skip this time consuming
step. Thanks.

But I don't understand why I should skip using starter fertilizer. I
still need to use starter fertilizer to encouraging the grass to
establish roots, and I still need to use some quick release fertilizer
to help the young grass seedlings to grow, right?

Jay Chan