I guess you're using ADO. Don't know much about it but I don't think that there'll be some major diferences (this uses SQL anyway).

So, if I got that right you first check if the file exists, if no, create a new table -> if that statement works, then it is ok.
Now with the export there's a little trick. I don't think your statement would work. You should create something like:
SELECT (fields) INTO [TypeOfDatabase; DATABASE=Path].[FlName] FROM Table;

So in your example something like this:
'st - string
'This just gets the Path. Didn't test it but should work
st=Left$(CommonDialog1.FileName, _
(Instr(CommonDialog1.FileName, CommonDialog1.FileTitle)-2)

Conn.Execute "SELECT TableName.LogNo, ...Duration, ...Time_s, ...Value_s INTO [Text; DATABASE=" & st & "].[" & sFName &"] FROM TableName;"

I don't know about INSERT INTO. Should work that way too.
Especialy pay attention to the Schema.ini file if you want specific output (e.g. delimiter etc.).

post back if not clear.