If you have problems with your phone, then I strongly recommend you to do a Factory reset. Since it has Android 2.3 Gingerbread, access Settings > Privacy > Factory Reset. It will wipe all the options, accounts, and custom files. Once the option is activated, the phone will restart and then you'll have to configure it again by setting the email account, Wireless network, etc. Add a Google account and then try to download again from Play Store.