In most cases monthly benefits start within about 45 days, and back due benefits are paid within 90 days or so. If there is workers' compensation involved, or outstanding debts to the government, or child support debt, I have seen payments take 4 to 6 months and, more rarely, longer.
If you do not have an attorney, contact your local US Senator's office and ak for help getting your benefits award processed. Senators' and US Representatives usually have staff who have their main job as trouble shooting SS or VA claims and getting benefits paid when approved.
Best of luck to you.
I concur with Attorney Farrell's succinct and accurate analysis of this situation. In my experience, the payment of back pay can take between 7 and 120 days from the date of the award.