The flash should certainly popup when the flash button is pushed and I think it's supposed to popup when needed in the "picture modes". I have a 20D which somtimes doesn't pop up the flash, but it's due to it sticking and if I give it a little help it pops up OK and it works OK.

My guess is that if it doesn't popup and when you help it manually it still doesn't flash, then there's probably an electrical problem.

Putting a bubble level on the hotshoe shouldn't have done anything to the flash, unless perhaps it had a metal foot which shorted out some of the flash contacts. That might cause some damage I guess. If it had an insulated plastic foot I don't see any way it could cause electrical damage. It could have caused some phyical damage though (especially if it was a tight fit) and that would lead me to suspect that....

...On some EOS cameras I know that there is a microswitch on the flash that can stick. This makes the camera think that there is an external flash attached, so it doesn't operate the built in flash. I'd guess this might be the most likely problem and if it is, you have to free it up.

I've attached a shot of the hotshoe of my EOS 20D. In that camera the microswitch is operated by a small while plastic "plunger" under the left side of the hotshoe. I'm not sure if it's in exactly the same position (or is the same color) on the 400D. However if it's stuck down, it will prevent flash operation and you'll have to try to free it up.

If the spring on the underside of the hot show rail on the camera has been bent, it could be holding the microswitch down, in which case you can just bend the spring a little. If there's something deeper down holding the microswitch closed, you may have to try to remove the hotshoe.

If it is the microswitch, and external speedlite should work just fine when mounted on the hotshoe. If you can't fix i it yourself, it may actually be cheaper to buy a small external speedlite (like the Canon 220EX) than to have Canon repair the camera! On top of that it will give you better flash exposure too.

I suggest you to get a better flash, 430ex or third party ones that can swivel and bounce.
I don't know if you can get cheap used flashes from ebay or online stores.
Those flashes are fun to work with. You'll certainly have more possibilities.

I never use built-in flash anyway, so if that happened to me I wouldn't be too much concerned.
I have a 420ex and pretty happy with it.