Don't let me discourage you from diving into BTC -- it can be a fun, amazingly-educational experience. But I know for sure that three months ago there was a tx-broadcast webpage already in existence. Unfortunately, I lost all my bookmarks and am trying to locate it again...
If you find the page, that's great! I think I'm still going to go ahead with this for the learning experience.
On the other hand, it may not be too difficult to setup such a webpage if you use the patch linked to from terrytibs: run an instance of the patched bitcoind, then make a webpage with a simple text-input box. The POST (?) command will simply convert the input text to binary, and pass it to your patched bitcoind for broadcast. You probably don't even need to know anything about BTC to do it! Just make sure there's someway to identify that there was an error... I imagine 90% of people trying to post txs in this way will have done something incorrectly the first few tries.
Sounds like we're thinking alike.
I'm going to give this a try.