To rule out any problems with you Perl code you could use sqlite3 from the command-line to verify your SQLite data file. For example you could do this to see what tables are available in your SQLite database:

plankton@chumbucket:~$ sqlite3 mysqlitedb
SQLite version 3.7.4
Enter ".help" for instructions
Enter SQL statements terminated with a ";"
sqlite> .dump
PRAGMA foreign_keys=OFF;
BEGIN TRANSACTION;
CREATE TABLE tbl1 (one varchat(10), two smallint);
INSERT INTO "tbl1" VALUES('hello',10);
COMMIT;
sqlite> .tables
tbl1
sqlite> .exit
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You can find out more about SQLite command line shell here: http://www.sqlite.org/sqlite.html