Help: splitting DNS records to web/email

I manage my domain's DNS records at my registrar. For that to work, I had set my domain NS values to the registrar's. Up to now I did not have a web presence, and I had all my email going to a commercial e-mail service provider. To do this, I had set my MX record pointing to the e-mail provider. Works OK.

Now I have subscribed to a web hosting provider for a web presence on a WIN Server 2003. Instead of delegating my primary DNS records to the hoster, I want to keep them at my registrar so I can still direct all my emails to the old email service provider.

My new hoster provided me with 2 NS values and their associated IP.
(There is no static IP assigned to my account with them).
I tried to point my www record, via A record, to the provided IP address, but I can not see my default site's page (when entering my site URL in a browser, one A record assignemnet gave me a mail server log in page of my hoster instead of my default home page, and the other produced an error page "no site found"). Earlier, instead of assigning the A records, I assigned the NS records to the descriptive NS values provided by my hoster, but then the browser could not resolve the URL (obviously, I am not an expert in DNS setups...)

I would appreciate some help in resolving this issue.

My domain is intelledyne.com

If 212.199.222.5 is the IP of your web hoster, then they haven't done anything on their end.
Anyway, What you been saying are way too confused, instead of using hoster/registrar, you should be explicit on their name.
Here is a question for you: Who should be hosting your DNS?

Thanks for the reply.

Being in a rush, I got a guru to help me out. I manage my DNS records at DOTSTER, and hosting my site at AGATE.CO.IL My hoster (AGATE.CO.IL) gave me two values to enter as my primary DNS:
NS1.AGATE.CO.IL (IP: 212.179.112.189)
NS2.AGATE.CO.IL (IP: 212.199.222.5)

Originally, I set up my DNS record as
www.intelledyne.com IN A 212.199.222.5
at the registrar's (DOTSTER) control panel, but this gave an e-mail login page of AGATE. I played a bit more (don't remember the details), and only got "no site is configured here" message.

The guru changed my records to:
www.intelledyne.com IN A 212.179.112.189
intelledyne.com IN A 212.179.112.189

and after propagation the site is now seen. He also said that the zone info at my hoster conflicts with my registrar's, and recommended that the hoster will remove my zone information from his system.

The term conflict might not be appropriate. Either one of them is authoritative for your zone. The other not being authoritative will not cause any conflict, it just won't be used. You can tell them to clean up their mess, that's all.