Given that this is NOT happening on all pages - but instead only on the home page - I would start by looking for conflicts between the elements that are being loaded onto the home page - which are not on other pages.
All the <A tags on the main page are causing a new page to open - not just the login and register.
This kinda suggests is something on the page thats getting messed up - and the obvious culprit would be some rogue javascript/
The Banner module springs to mind as the most likely or the jquery core.
On your home page the jquery core library is being loaded 3 times from two different locations.
Looking at the files that are being loaded both version v1.3.2 and v1.5.2 are being referenced - doing this can potentially
lead to all sorts of problems.
<script type="text/javascript" src="/Portals/0/Skins/OncUViewHomepage/jquery.min.js"></script> <---- a local version stored in your skin v1.3.2
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1/jquery.min.js" type="text/javascript"> <----- the global version stored at googleapis.com v1.5.2
<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1/jquery.min.js" > <----- the global version stored at googleapis.com v1.5.2
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I have seen all sorts of wierd things happen to pages like this - I would start by looking in this area
Westa