I cannot find anything related to either basemre.dll (except your posts). Usually that's not good because malware often make up new names for themselves when infecting a pc.

I would still suggest submitting that dll to a multi scan site to see what other scanners make of it.. both to confirm it's actually malware and to find other names for the virus because that name above also garners no hits.

http://www.virustotal.com/

Also, let us have a look at the hijackthis log.