“Sweet Charity” gives new meaning to the word “revival.” After producers canceled its Broadway run and shuttered the show in Boston on Sunday, the much-troubled production is now back on the burner. “Sweet Charity” begins previews April 18 and will open with its original star, Christina Applegate, at the Al Hirschfeld Theater on May 4. It is the last day a show can open to qualify for this season’s Tony nominationss. Applegate broke her foot during the show’s Chicago engagement prior to the Boston tryout. Charlotte d’Amboise, who replaced the injured star in Boston, will perform the first six days of previews in New York City.