1. Don't get frightened, explain your situation to your current employer and try to convince them to relieve you in 20 days
2. Immediately inform your recruiter about your situation with current organization and ask is there any possibility to extend your joining date.
3. You said that it is a reputed company, so BGV(Back Ground Verification) process must be there in your offered company and to finish your BGV for them it will take a minimum of 21 days(Because Criminal check will take time on this process)
4. From your end try to help your current organization atleast in replacement of your position, you should have an idea who is working same like you in your field, it is not a TDS job.
5. Try to collect the check from your client because you are telling that it is pending since long period so you must hav eteh rapo with them as you are working for thsi company from long back. From your end you should not deny to respond properly with in this 20days.
18th September 2014 From India, Visakhapatnam