Google Play Problems:

I have an IMac and the operating system is Mac OS X 10.6.8 Snow Leopard. Everything was fine until I downloaded "Google Play". 

I downloaded "Google Play" and sent (uploaded) all my 4500 ITunes songs to the cloud called Google Play. This took 4 days to upload, because Google Play is a very slow program.  My IMac has been messed up since:

1)  Everything now is super - super  slow.

2) Cannot restart or shut down my iMac computer. Get a message that I must quit Safari first.  But I can't quit safari because the quit safari option in the menu is always grayed out now. So the only way I can shut down or restart is to manually shut off the computer, which may harm it. And when I click the button or switch to turn it back on, the problems and the trash dialogue boxes (see #3 beow) remain the same.  

3) cannot move anything to the trash. (I am trying to empty the cache in the library to speed up the computer.) I just get dozens of trash dialogue boxes that say "preparing to move to trash" but this goes on forever and nothing is moved to the trash. And I can't get rid of these dialogue boxes that say "preparing to move to trash". There are loads of them and they stay forever.

Some things I try to move to trash but I get a "copy" dialogue box with the message "Prepare to move to desktop" and that message goes on forever also.

Or it says "Preparing to move to "com.apple.AddressBook" but nothing happens. 

(the last one - "com.apple.AddressBook"- is one I had tried to move to the trash).

Shutting off the computer does not help. These trash dialogue boxes are back when I turn on the computer.

4) Trying to speed up computer by going into Utilities (Finder/Go/Utilities) and then clicking on Disk Utility, then McIntosh HD, and then "verify disk". This is supposed to speed up the computer. But when I go into Utilities the Utilities dialogue box is empty - there is no "Disk Utility" to click on. There is nothing there, except a small spinning circle in the bottom right of the dialogue box that looks like it is trying to do something, but nothing ever happens.

5) Can no longer save documents. If I try to save a new document, it does not show up in my documents folder.

IMaybe the 4 days of uploading  filled my IMac with all kinds of spyware and that messed things up.  Who knows?

I do have Intego VirusBarrier 6, and have had that and their previous version VirusBarrie 5 for a few years. I ran a full scan and it found only one new virus besides the 2 I previously had adn that were already in quarantine  I put the new one  in quarantine.

 Is there anything I can do?