Sharepoint 2003 Searching

1. Should always use ie security zone intranet when adding sites....However, this setting has nothing to do with search....
2. Please ensure that your public URL has an  AAM setting preferably Extranet

Can you please be a little more specific

please ensure you have alternate access mapping setup up the right way and please make sure you have the intranet/site has been added on ur trusted internet or intranet zone providers in internet explorer

I'm still getting the same error

Ok, Try adding the machine name to the host file and do a iis reset, reboot would be recommended.
then try search again
just read thro this as well http://texhex.blogspot.com/2008/09/windows-search-server-sharepoint.html

Ok, I am almost there.

One thing.
I don't need to edit any AAM, I need to add

http://sharepoint1
https://sharepoint1

add your machine name to your AAM and under default/intranet zone

What do you mean by this
" default/intranet zone" not sure

first add your machine name to your Alternate Access Mapping under intranet zone provider.

Remember I have a working site already, so it's there already.
I am just adding a new site because at some point we will be removing the first site.
for example.

1st: site:  sharepoint.companyname.com ( this is already working fine can searching is working perfectly)

2nd site: sharepoint2.companyname.com (we added this site recently but unable to perform searches)

Both sites is exactly the same thing.  We want users to now user sharepoint2.companyname.com and be able to search.
Remember, both sites are the same but different url.

Just wanted to make that clear.

Thanks

Ok, I did it and it worked!!!!
Yes.....

When you are adding an AAM and it maps to a "public url for Zone, what does that mean"

Issue resolved.
All these expert comment was extremely helpful,  
Thank  you

Why is it that users and being prompted to enter password now everything they try to access sharepoint.  Thanks

please check the settings on the browser intranet zone,under user authentication-> automatic logon for intranet zone

Fantastic.  Issue resolved.
Thanks again

Thanks for all your help but one more question please.

1st: site:  sharepoint.companyname.com ( this is already working fine can searching is working perfectly)

2nd site: sharepoint2.companyname.com (we added this site recently)

Issue:

But when users go to sharepoint2.companyname.com it redirects to sharepoint.companyname.com, the original site.

How can we not have the site redirect to sharepoint.companyname.com, but function independently.  
Please help