Internet explorer 7 security warning errors.

Do you have the exact text/wording of the warning in question to post here?

I am sure you have tried this but just in case. Did you go under tool --> options ==> advance and rest all the IE settings to default . May sound like a simple fix but I over looked this when I was having the same issue.

Is this system in the same setup as the others you are referring to? i.e. both systems are members of the domain? Will also await the answer to Yobri's question to get a fuller picture of the situation.
The error should tell you what the issue is, i.e. signing authority is not trusted, the name on the certificate does not match the name you used in the browser, etc.
IE 7/this system  may have an outdated intermediate certificate for Verisign that expired.

Have you made sure that your system time is correct?

you can upgrade to IE8 - see if the problem is gone then

here it is :  http://www.microsoft.com/downloads/en/details.aspx?FamilyID=341c2ad5-8c3d-4347-8c03-08cdecd8852b

@ yobri: exact error message " there is a problem with this website's security certificate.....The security certificate presented by this website was not issued by a trusted  certificate authority"

steeler4life : I have reset all the IE settings but of no luck.

@arnold: The pc's are in same domain. I have also copied the intermediate cert from another PC which has no issue but still it doesn't work.

@walrussoup : The system time is network time. no issues.

@nobrus: tried upgrading already to IE 8.. but was of no luck.

Look at the certificate chain to determine which certificate on this computer is causing the problem, then you can user the certificates MMC to see whether you have the wrong certificate in the chain of trusted.
Is there a site that can be included here so we can see what the issue might be?
The likely issue is that the certificate on this system is an intermediary that expired and you need to replace with the updated/valid one.  If you go to windows updates, under optional updates, is there a root certificate update?  See if you use it to update your system whether the issue you are dealing with goes away.

Who signed the certificate with which you are having problems?

All my previous comments dealt with the issue that your certificate store was at fault.
In my last comment, I suggested you do exactly that.