TRACON Controller described a loss of separation event during multiple equipment failures; complicated further by challenging weather conditions.

Narrative

A B737 and a Learjet were on vectors; opposite direction to one another at 5;000 FT. TRACON was experiencing multiple system failures during the event; including failures of most instrument landing systems; due to a snow storm. During the event; traffic volume and complexity moved from moderate to heavy. Several aircraft were reporting erroneous information on the ATIS as they checked in. Specifically; the ATIS was advertising that the runway in use; at the time; was closed. Also; due to the failure of the ILS at ZZZ; we were on an RNAV approach. The RNAV approach required a certain RVR; which several aircraft inquired about; however; the RVR equipment also failed; adding to the confusion and frequency congestion. I allowed myself to become somewhat distracted by these issues; as well as attempting to verify what was being advertised on the ATIS through the FLM and trying to get visibility information through a PIREP. I then began to lose separation between the B737 and the Learjet. I attempted to issue and immediate right turn to the B737; but my initial attempt was blocked due to the frequency congestion. My second attempt was successful; however; by this time separation was lost. Recommendation; ATIS information that kept up with the rapidly changing conditions would have helped. I also question the prudence of running an RNAV approach; which is contingent on a reportable RVR value; when the RVR reporting equipment has failed.