Q: Computer connect to the itunes store?

Problems connecting to the iTunes Store often stem from issues with the Windows firewall or a firewall in a router, a privacy filter (such as McAfee Internet Privacy Service or Norton Internet Security), an antivirus/antispyware utility, or a download accelerator. Start here:

iTunes for Windows: iTunes Store Connection Troubleshooting

iTunes for Windows: Connection Issues when using Internet Filters, Accelerators, or Firewalls

iTunes for Windows could not establish a secure connection to the iTunes Store

iTunes for Windows: Possible iTunes Store Errors

for some basic tips to start isolating the cause of the problem. What you may need to do is temporarily disable any such service and see if that fixes the problem. If so, then if it's a firewall/Internet filter that's causing the problem and you'll need to set the offending service to allow iTunes to connect to the iTunes Store.

Hope this helps.

when I try to connect to the store, the progress bar shows it's trying to connect but the computer won't finish connecting to the store.

If it's endlessly saying "Accessing iTunes Store" I'd try the following document:

Apple software on Windows: May see performance issues and blank iTunes Store

(If there's a SpeedBit LSP showing up in Autoruns, it's usually best to just uninstall your SpeedBit Video Accelerator.)