Is their a way a person can open their own store on the internet without eBay & without breaking the bank?:o

Definitely. Time for links a plenty...

Online Store Packages
http://www.oscommerce.com/
http://www.cubecart.com/site/home/
http://www.zen-cart.com/
http://www.actinic.co.uk/ - Not free but have a 30 day free trial

Ways of getting payment
http://www.paypal.com
http://www.worldpay.com - Not free but v.good

As for some general getting started guides, I'd take a look in your local newsagents for some internet magazines like .Net or Practical Web Design magazine (if you are UK based anyway) - they often have articles on this kind of thing and can give you some suggestions. Plus there is always good ol' Google.

Getting a store on a WEB site is relatively in expensive. It can be done for under $1000 (USD) in most cases.

The problem is getting people to come into the store. That advertisin or marketing may double or triple the cost of startup.

I have my own store website. It costs me a little under $100 a year to maintain. That includes hosting, the domain and SSL certificate. I use zen cart and love it. If you have little computer experience you can find many online hosted shopping carts that come in a range of prices.