Unfortunately no. To enter a business lounge you need to produce a departing boarding pass showing business class travel (there are exceptions like airline status, or being Qantas club member). Arriving travel does not count. You are only entitled for business class lounge before your EK flight.
If it’s any consolation, Changi has free movies, free swimming pool and free wifi, as well as free computers (but they are extremely slow and timed to 15 mins per session). And of course a lot of shopping. Also if you have long hours between the flights (I think at least 6 hours), you can get a free tour of Singapore.