it would seem if you never got a corrected w-2, H&R has not filed your return. If you used Turbotax without a corrected w-2 (w-2c) when you went to e-file it would have been rejected
I'm not sure what H&R could tell the IRS you need a w-2 with your correct SSN (w-2c). follow through with your ex-employer and H&R.
Block didn't "tell the IRS" anything ... there is no way they can. What they did do is simply filed the return using the W-2 with the incorrect SS# on it and told YOU to have this corrected by the employer. Now if you did as directed and the employer did not file a corrected W-2 form with the SS administration (who shares this info with the IRS) and did not send you a corrected copy then you will need to contact this employer to "light a fire under their butts" to get it done.
Until the corrected W-2 form is filed the IRS cannot confirm the infomation entered on your return for wages and withholding. Thus the return will be stuck in processing until they can which means they get the corrected W-2 form from the employer.