Can I run a SQL 2000 database integrity check and database backup without locking up the database?

I'm thinking the answer is no, but I need some confirmation.  :)  Is it possible to run a SQL 2000 database integrity check, followed by a database backup and still have the database accessible?  Right now I believe the database is getting locked up during both processes.  We are now running a third production shift during the time these are scheduled to run.  I know very little about SQL so I thought I would just verify what I suspect.  Thanks so much to any help provided!!