Is there a statute of limitations on a pending application of warrant?

3 years on a felony .. unless you murdered someone in the process of the gun possession your outside the statute of limitations. It remains on your arrest record unless you try to expunge the arrest record

If there is a warrant there should be a charge filed and that stops the runing of the statute of limitations

The statute of limitations should have run out some time in 2004. You should speak to an attorney about getting the arrest expunged from your record. You may or may not qualify for an expungement based on other factors in the statute but it is worth talking to an attorney about.