I am very disappointed in it and may even return it to the store if they will give me a refund.
I would recommend that. An LCD without a digital input isn't worth keeping.
it is possible to connect a crt and an lcd on the same graphic card?
Yes, it is.
It has an analog and digital output, so I guess with a converter of some sort it is possible, or am I wrong?
Actually, if you had an LCD with digital-in, you could have the LCD on digital and the CRT on analog. Otherwise, you would need a DVI to VGA converter, and then you'd have two analog-outs, one for each monitor.
What results would that bring? Same image on both monitors at all times (unless one is turned off)?
I don't know what options your graphics card has, but on mine, you can do that, or you can have a wide image span the horizontal lengths of both monitors, or a tall image span the vertical lengths of both monitors, or have two separate desktops, one for each monitor, with the capability to display different things on each monitor, and you can drag windows from one monitor to the other. I use the latter option.