LazyOneLazyOne says (pasted from a comment which the original poster indicated solved the problem):
As far as I remember the server name (domain name) used when Magento was installed is used when building/requesting URLs. You do not see it when accessing
.html
file as it is static file, but you see it when accessing Magento-powered PHP file. Check the Magento settings for localhost and replace all occurrences (except DB and similar) withstore1.no-ip.biz
. At least this is what I was doing when moving Magento from local to live server when I was using it.