Hi Nina,
Internal speakers that produce the POST (power on self test) beeps are usually supplied, or built into the case at the time of build. If one isn't supplied with the case, they are often not added in by the system builder. Many people don't like the "annoying little beep sound" anyway so they don't miss them until they find out that they can be a handy little diagnostic tool

Your motherboard layout should look something like this, with an internal speaker (if supplied) connected to the pin header shown:
If you don't have one, I have a few spares here that I can help you with so don't stress!
The GTS 250 cards also need additional power from a y-adaptor cable, which should have been supplied with the card, something like this:
Make sure that it's securely inserted into the graphics power connector at the end of the card, or it may be suffering from power issues

Under full load, your card should consume around 220W of power, so the 650W power supply
should be enough, depending on how many other devices you have attached, it's component quality and actual power output.
I got distracted halfway through typing this post up, and my apologies if you've already tried this, but before you re-inserted your graphics card in question, did you give the contacts a little clean up first?
If not, it's pretty easy to do, but you do need to be careful...
Unplug the power cable at the back of the pc and then take the side panel off the case. Touch the bottom of the metal case to ground any static electricity from your body, then unscrew the graphics card retaining screw and remove the card while pushing the retaining clip in at the end of the PCI-E slot (if present).
Carefully put the card down flat on a non-metallic surface (anti-static bags from computer parts are handy for this).
There's a few products you can buy to clean the contacts, but if you're careful, you can use a clean pencil eraser. Gently polish the gold contacts on one side of the card, turn it over and do the other side, then use a clean, lint free cloth to wipe away any little rubber dags that are left behind.
Ground yourself again by touching the inside of the case, re-insert the card, ensuring that it's seated propoerly and the retaining clip is doing it's job, re-connect the y-adaptor power cable, connect the PSU power cable at the back, power it up and check it out.
Let us know how you get on
