This post adds to almut's post in case you want more details on compilation and execution order. If you don't, then skip this post.

use Module;
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is the same as

BEGIN {
    require Module;
    Module->import();
}
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(In fact, in existing versions of Perl, the parser can't tell the difference and that's the source of a bug unrelated to this post.)

BEGIN blocks are execute as soon as they are compiled, so

push (@INC, "D:\\Perl\\site\\lib");
use DBI;
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is executed as follows:

1. push (@INC, "D:\\Perl\\site\\lib"); is compiled.
2. require DBI; is compiled.
3. DBI->import(); is compiled.
4. require DBI; is executed (by virtue of being in a BEGIN block).
5. DBI->import(); is executed (by virtue of being in a BEGIN block).
6. The rest of the program is compiled.
7. The compilation phase ends and the execution phase begins.
8. push (@INC, "D:\\Perl\\site\\lib"); is executed.
9. The rest of the program is executed.

As you can see, the modification of @INC happens much much too late.