Upvote:3
Changing your passport does not change who you are and will not make any difference to your chances of entering the UK.
Edit: The section below is not correct. As noted in comments, you do have an overstay record which will be considered in any future application.
[It sounds from your description like you don't really have an adverse history; when your application was rejected, you complied with the rules and left the UK.]
You can apply for a visit visa and as long as the visa office is satisfied that you meet the criteria, you will get a visit visa. You will need to show ties to your home country, such as having a job, and that you have enough money to pay for your trip.