Hi,
It sounds like you are on the right track. curl should do it.
A link to check out is:
https://en.bitcoin.it/wiki/Running_Bitcoin
In the Windows section, of note is:
Batch automation
To work with batch, you have to start the daemon (bitcoind.exe). The bitcoin.exe run with option "-server" will respond with GUI-messages you are not able to process its answers.
I believe they are using "batch" to indicate the RPC server interface.
So it appears you'd want to run something like this which is similar to Linux:
bitcoind.exe -server
My guess is that you did something like
bitcoin.exe
or just started it from the desktop which I don't believe starts the RPC interface.
Alternatively you could use the server=1 in the bitcoin.conf file - the appropriate location is detailed on the link below. I don't run it on Windows, but in the bitcoin.conf file you'd want to add a server=1 option see the link above if you don't use the command line option.
You will also need to set your rpcuser and rpcpassword in the bitcoin.conf file (or the command line perhaps, but I think the .conf file is preferred).
Hopefully that will help a little....let us know! ;-)