If этой refers to the current week, what does the verb being in the past tense mean or imply?
Let's draw a timeline:
Beginning of the current - - - - - now - - - - - End of the current week/month/year (or today) week/month/year
Using the past tense you cover the time span from the beginning until now:
На этой неделе я была дома.
This means that you were staying at home from Monday till now (today).
Using the future tense you cover the time from now until the end:
На этой неделе я буду дома.
This means that you are going to stay at home from now till Sunday.
Using the present you are talking about the whole time from the beginning to the end:
На этой неделе я (сижу) дома - I stay at home this week.
Normally you use the past tense near the end of the time scale and the future near the beginning. "На этой неделе я буду дома" being said on Friday would be very unusual.
At first, let me to correct your sentence. "На этой неделе я была дома, никуда не ездила." Because "Я был" if I'm male and "Я была" if I'm female.
If you say "На этой неделе я сижу дома" it means that you are sitting right now (like present continuous in English. Example: "Today I'm sitting home."). It starts on Monday (or Sunday, it doesn't matter) and ends on Sunday. If you say "На этой неделе я сидел/сидела дома" it means that you were at home last week. Like today is Saturday, you are going to the cinema, but for a whole week between Monday and Friday you sat home.