So what's different between now and the previous question? If you only want data from the previous 24 hours, you can add a restriction to your filter that only searches data from within the previous 24 hours.
Also, you can possibly re-use your previous measure, applying a different context:
You're FILTERing Table1 and only calculating [MeasureThatWorks] on rows where the DateTime is after (NOW - 1 day), which is 24 hours ago. Feel free to edit the filtering expression to include/exclude data as you see fit.
If you wanted data from the day before yesterday, you could change the condition to
[DateTime] < NOW()-1 && [DateTime] > NOW()-2
Which returns data where the datetime is earlier than 24 hours ago, and after 48 hours ago. You can change it to only use data that fits whatever condition you describe.
I don't remember the original measure we ended up using, but it's because that measure grouping them by the value of HOUR(start time). It can distinguish between 23 and 1 easily.
However, it would NOT distinguish between 2300 on day 1 and 2300 on day 2. We got around this by limiting the query to now - 24 hours, so the same time can't appear twice. If you wanted to be more specific, you could explicitly group by both hour and date, so that there's no chance of data from different days mixing.