Heh. SQL is not an API, it is a protocol. The Windows API for SQL is simply a Microsoft-ism. Any SQL-capable server will accept queries in text form by some means or another. Here is a primitive example of an SQL statement:
[tt]
SELECT PhoneNumber FROM PhoneBookTable WHERE LastName = "Smith"
[/tt]
As for TCP from QB, it is basically not worth trying. There are timing issues that must be handled continuously in the background to maintain a PPP connection over dialup. It is possible, however, that a terminal server could be used. In this case, the QuickBASIC program would talk to a server in much the way that a terminal program communicates with a BBS -- a plain text link. An account could be created on a Unix server that would, upon successful login, allow essentially direct access to the SQL server, and the QuickBASIC program could then issue SQL statements through the COM port. This would require substantial setup on the server side, but it would be just one time, of course, not once for every client machine.
As I mentioned earlier, I believe maintaining a PPP connection in the background with active TCP connections inside a QuickBASIC program with an active user interface is, while not impossible, somewhat of a lost cause. It would require more effort than is really worth for such a project at this point. While a packet driver could do the trick, I still think it's easier to let a terminal server handle the input.
Note that Unix would not be required: a Visual Basic program (as suggested earlier) could be used to accept incoming modem connections and relay the SQL statements to the server. This would still not require TCP connections from a QB program. I believe this route would be preferable.
If not all client machines are within local calling range of the server, it may be possible to find a local ISP that will allow such terminal server access. At the very least, a telnet command could be issued through the modem link by the QuickBASIC program.
Anyway, this is all based on speculation of information not available regarding the situation.