MacMail displays layout but does not receive incoming a force quit shows red Mail (not responding); Apple support 2 hours and the same result 3/22. Can it be a startup issue? Support says I need to get a new IMac. Is OS 10.7.5 Lion,2 GB Mem, 1.16 GHz

On 3/22 My Mac Mail displays layout on screen but nothing fills and no email comes in as a small circle continues to circle. Force Quit shows the Mail in red with (not responding). 2 hours with Apple support including a reinstall of my OS 10.7.5 Lion and no change. Support thinks I need to go up but I will need to buy a new IMac to do that. Still I would need to move existing email to the new one. Could it be a startup file issue? I have a Late 2006: Processor 2.16 GHz Intel Core Duo, Memory 2 GB 667 MHz DDR2 SDRAM. I have stored email I really need to access at times. Thank You. I can pay something if needed.