The 1600 has been a buggy card since the get go. A quick search with Google will tell you that many many other people have exactly the same problem as you. The general consensus is that the cooler/fan is no longer working (does the card fan startup?) as you know, the card will stop your system from even starting to prevent damage to your cards chip.
If you want to stay with ATI, the X1950 Pro is really a good choice, again the cooling fan is the weak point but it should maintain 50-55 degrees loaded. If that worries you, you can get an artic cooling fan which replaces the stock fan (£15 here in the UK). Much better.
End of the day, you current card is fried.
