Do not rush to factory restore before looking into things further, especially if your unit shipped with software 1.0.
AppleTV1 was never designed to run completely standalone - it is linked at the hip with iTunes.
AppleTV1 was designed to be synced with media from iTunes which appears in My Music, My Movies etc.
If it's full and iTunes is running you will also see content under My Music etc that will stream from the computer on demand provided itunes is running (unless you turn this option off in iTunes).
When configured to sync with iTunes AppleTv goes into an Auto sync mode where it decides what to copy over to the unit - so unwatched material before watched etc. You can customise this if you want under various Device Settings tabs displayed when selecting an AppleTV Device in itunes (left hand side) - do you see an icon? If not it may not be synced to this itunes.
Later the ability to purchase directly arrived too, but the idea was for purchases made on the unit to sync back to iTunes to keep the devices 'in sync' and to allow for backups. The trash can I believe only appears for items purchased on it. so you could manually delete them.
There is also a streaming only mode to connect additional itunes libraries on other computers 'My Shared Music etc'.
See here:
http://support.apple.com/kb/HT1143
Previously if things you bought on the unit did not sync back to itunes and AppleTv failed or there was a problem with 'reverse sync' (my term) that prevented it working you might not be able to salvage that content and could not redownload it.
We need to know what software version you have - Settings>About (3.02 is the last one), and if you have the unit synced with iTunes still - does an icon appear in itunes under Devices (right click it and Transfer Purchases if you can to copy stuff over to iTunes bought on the unit directly).
Last year/early this year Apple has sensibly allowed users to redownload any previous account purchases from the itunes Store in itunes - ensure you have latest version of iTunes and navigate to teh store home page - on the right under Quick Links you should see Purchased - here will be a list of things you can redownload for free under that itunes account. The catch? So far movies only available for redownload in the US and not all studios are on board. Other content can be redownloaded in many countries, but if an item is no longer in the store or has changed somehow (think of a change in the product code) it won't be available. Check here to see what you could salvage by redownloading for free.
Factory restore will put you back to shipping software and delete any synced media from the unit - some say purhcases made on Apple TV remain if not 'reverse synced' but I would not rely on this unless it was a last resort to restore it.
AC