Banks are so becoming desperate for checking customers and fee income that they have returned to an old-school advertising method: prize giveaways. And they seem to be working. Boston-based First Trade Union Bank has opened 230 checking accounts this year by offering consumers a chance to earn $100 in cash bonuses. Boston's Eastern Bank offers new checking account customers in April and May four hours of house cleaning services valued at $165. At East Boston Savings Bank, consumers can get a charcoal barbecue grill or a beach chair. The campaigns are aimed at consumers ready and willing to switch financial institutions -- about 15 percent of the market.