Ok, looking at what you have, the INNER tables are sufficiently 'tabular' I'd say sure, use a table on that... but your OUTER tables, and in fact most of the tables on your page serve NO legitimate purpose. The table around the H1? Pointless. The table around the other tables? Pointless.
Of course, your original has two doctypes, so that's kinda funny.
Sadly, when most people "learned" HTML 4.01 they never actually learned HTML... there were so many bad practices and pointless coding methods still in circulation, nobody back then was able to even learn what HTML is or how to use it right; a trend that sadly continues to this day.
One of the keys to learning to use CSS is rethinking how your HTML is built... particularly if you learned the -- what we now call sloppy and bad -- method of building sites with endless "table for nothing".
... even using tables -- you seem to have multiple tables doing the job of one table -- you have no relationship between the rows, they're multiple tables side-by-side for... well, I don't know what for. If everything is on a row, put them in a TR, if that means empty TD, so be it. Empty TD is certainly better than trying to make multiple side-by-side-by-side tables line up with each-other.
Even back then, you've got a whole slew of markup for nothing, and most of it is tables for nothing; that page should have -- by my reckoning -- six tables for the actual tabular data; there should be no tables inside tables, H1 inside tables -- hell if you're going to use tables the heading text for each table you have inside <br> should be a CAPTION.