CL65 CREW HAD THE ACFT WX RADAR FAIL WHEN BEING VECTORED TOWARD CONVECTIVE ACTIVITY.

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DEPARTING S OUT OF TULSA; OK; WE WERE ASSIGNED TO A NE HDG AND NEW ALT OF 15000 FT BY TUL DEP. WE WERE THEN TOLD TO CONTACT ZKC ON A NEW FREQ. AS I WAS TURNING THE ACFT NE; MY FO AND I NOTICED A CUMULUS LAYER OF CLOUDS IN THAT DIRECTION. I ASKED MY FO TO TURN THE WX RADAR ON TO LOOK FOR ANY PRECIP. AS HE DID; WE IMMEDIATELY RECEIVED A RADAR CTL FAULT MESSAGE WHICH MEANT IT WAS UNRELIABLE. WE QUICKLY TRIED TO ESTABLISH COM WITH ZKC SO THAT WE COULD GET VECTORS AWAY FROM ANY CUMULUS ACTIVITY BUT WERE UNABLE TO ESTABLISH CONTACT WITH THEM. AS WE CONTINUED THE CLB TO OUR ASSIGNED ALT; THE ACFT BEGAN TOSSING AND TURNING UNCOMFORTABLY INTO THE CLOUDS. WE RETURNED TO OUR ORIGINAL RADIO FREQ AND INFORMED THE PREVIOUS CTLR OF OUR SIT. HE STRONGLY SUGGESTED THAT WE TRY THE ASSIGNED FREQ ONCE MORE. WE ACKNOWLEDGED HIS REQUEST BUT WERE STILL UNSUCCESSFUL ESTABLISHING CONTACT. AGAIN; WE RETURNED TO OUR ORIGINAL RADIO FREQ AND STRENUOUSLY REQUESTED VECTORS AWAY FROM THE CONVECTIVE ACTIVITY AND THAT ZKC WAS NOT ANSWERING OUR CALL. REALIZING THE SIT WE WERE IN; HE FINALLY VECTORED US AWAY FROM THE ACTIVITY AND REQUESTED THAT WE TRY THE SAME FREQ HE HAD ASSIGNED US AGAIN. AFTER A THIRD ATTEMPT; WE WERE FINALLY ABLE TO ESTABLISH CONTACT WITH ZKC AND RECEIVED FURTHER VECTORS. DESPITE OUR UNRELIABLE RADAR; THIS EVENT COULD HAVE BEEN AVOIDED IF ATC HAD BEEN MONITORING THE WX AS THEY WERE VECTORING US OUT OF TULSA AND TAKEN THE TONE OF OUR REQUEST AS A SIGN THAT SOMETHING IS WRONG; EVEN THOUGH THEY WERE INFORMED OF OUR SIT.