First, stop using the task killer. Android has a pretty good task killer installed and task killers can destabilize your phone if they kill an app that the system needs. The Android task killer knows better than to kill these apps. Lots of apps loaded in the background memory is fine as long as they are not taking CPU cycles. Android will kill apps as it needs memory, and it kills apps in order of least used apps, first. Unfortunately, there's nothing you can do about the stupid spiderman game loading (without rooting and I wouldn't suggest a brand new Android user dive into that just yet).
So, uninstall the task killer, reboot, and try doing using the phone like you have been. If it keeps doing the screen blank out thing, have Sprint repair store check out the phone. And make sure it's a Sprint store with repair capabilities. Go to sprint.com, find a store near you, filter for repair centers, and only go to ones that say "Sprint Store" instead of "Sprint via so-and-so" because the so-and-so's suck and will likely give you the run around.