Sakon, that's a bit confusing. Having two cards named Staryu in two different sets does not consitute a reprint of the first Staryu. The whole point behind a
reprint is that the card is
printed again, hence
reprint. Base Set Staryu hasn't been
printed again, so you can't use it.
You're not allowed to use any cards from sets below the cutoff line for Modified format. Currently, that cutoff line is EX Deoxys. Cards in sets before EX Deoxys are not allowed for POP-sanctioned, official tournaments.
You
can, however, use older cards (as in anything that was released before EX Deoxys) if the card is reprinted in a Modified-legal set. This is known as the reprint rule.
Base Set Staryu does not match any current legal Staryu in Modified, so you cannot use Base Set Staryu in any deck. They are not the same card, even though they share the same name. In order for you to be able to use Base Set Staryu in an official tournament, a Staryu card that matches the Base Set one
exactly would need to be reprinted in a set that is legal for the current Modified.
Even if two cards are strikingly similar, unless they are
exactly the same in every aspect, you can't use the older version of the card.
Take a look at Pikachu from POP 4. It is the same card as
this Pikachu from Jungle. The only difference is that on the POP 4 card, Spark costs [L][C], and the Jungle version's Spark costs [L][L]. Even though they vary by a single Energy, it's enough to make them 2 completely different cards, and therefore the Jungle one is illegal.
Here is the official ruling on Mysterious Fossil.
The Compendium said:
== MYSTERIOUS FOSSIL (Fossil Expansion; Legendary Collection; EX:Sandstorm; EX:Legend Maker)
Q. The new Mysterious Fossil trainer from EX:Legend Maker now has 50hp rather than the old 10hp versions. Does this mean that I now play the older versions as 50hp too?
A. Yes it does. Treat all Mysterious Fossil cards as if they have 50hp. (EX:Legend Maker FAQ; Feb 16, 2006 PUI Rules Team)
Fossil Mysterious Fossil's text is the same as the Legend Maker one; the Legend Maker one contains clarified, updated wording. It meets the criteria for the reprint rule, and so you can use old ones in your decks as long as you treat them as if they were the newer version of the card.
Going back to Staryu, the Delta Species Staryu is not a "newer version" of the Base Set one. They're two completely different cards, and that is why the Base Set one is still illegal.
Does this help?