If you cant download, use the "Downloads" app. If you're on wifi, there's an option to download over wifi. If you're on mobile, it will ask to download over mobile. It basically won't go until you tell it what to do. Just drag the notification bar down, select the download, you'll go to the "Downloads" app and then tell it what it needs to be doing.
If you don't have the "Downloads" app (Tyrone), update to a GB-based rom to get any sort of troubleshooting help. Hardly anyone is on the deprecated FroYo model anymore. I strongly encourage, and advise, you to move up.
Augoza, if you've tried the downloads app and you're still having some issues, you can try going to Settings > Programs > All > Market > Force Close > Clear Data & Clear Cache.
Then try downloading and seeing if that helps.