I can't answer your question because .. One: Is this a game that you have downloaded to your Facebook account or is it on someone else's page?

Two: Does the game require Flash of some sort?(you didn't say)

Three: What exactly have you installed and un-installed numerous times?

I have put the link to bejeweled's homepage where you should be able to play it.

Since you can only put one url link in these messages, my next post will give you the other link that may help.

Here is a link that might be useful: BEJEWELED

Hope this helps.
If you can provide anymore information than you already have on your problem .. maybe I or someone else can be of further help.

Here is a link that might be useful: Google Bejeweled

OK

I looked further into your problem and found the "Bejeweled Blitz" that you are talking about on Facebook.

You need to download Flash 10 to play.

I have provided the link.

Here is a link that might be useful: Adobe Flash 10

I will caution you on using any of those type applications on a facebook page it is much safer to go to the actual game site home page and play there, any app like that on facebook can be and have often been altered to infect a users pc by changing the scripting of the app. I urge people to NEVER use any type of 3rd party app on facebook or any other social networking site, people set those things up specifically to entice people to use them and get infected.

Since you have been using them I would urge you to download, update and run a full scan with malwarebytes free to see if you are possibly infected.
Malwarebytes' Anti-Malware

for a reality check just go to google and search for facebook virus for just a few of the many types of infections out there. Facebook and my space are a hackers dream land.

Very Good Advice ravencajun!