Most PC's have multiple sound output sockets.
In normal standard PC's you plug your headphone in the same socket as you would plug in active* speakers since the output signal is not amplified.
With some soundcard outputs there is a difference between the sockets for the line-out and the headphone socket. The socket of the line-out is already amplified whereas the socket for the headphones is not.
When you plug in active speakers into an already amplified socket outlet you'll get distorted sound (and in the worst case scenario you can blow up your speakers).
*"Active" speakers are speakers which have their own amplify system; you need to plug them into a power outlet also (most PC speakers). "Passive" speakers do not have an internal amplify system, they need to be hooked up to an amplifier (eg: most speakers on a HiFi system).
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This said, you didn't provided enough information though.
When you speak of your "hi-fi speakers", do you plug them directly to your soundcard on the PC? Or do you plug your hifi system (aka amplifier) to the soundcard (and thus the hifi speakers are connected to the amplifier, not to the soundcard).
What is the "playback slot"? What is the proper indication (name or pictogram) printed above that socket?
And by "phone cable" I assume you mean "audio cable", as a phone cable is cable you use to plug your telephone into the phone wall socket of your home 
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1) Set your sound configuration for your PC to normal (do not adjust anything like bass, treble, etc... set everything to normal/default). Don't forget to check your specific sound driver settings (Windows' own configuration panel is useually not the only control panel for the sound!!!)
2) Do the same for your HiFi system. Set all the bass, treble, midtone, etc at the normal level (useually indicated by "0dB"). This could also mean turning off the "Bass Reflex", "Bass Boost", or whatever other special FX options you might have on the HiFi system.
3) Connect the "Line Input" or "Aux In" from your HiFi system to the "Line Output" or "Aux Out" (not headphone socket if you have a seperate socket for that!!)
4) Connect your speakers to the HiFi system's speaker output. Do not connect them to "Line Out" or whatever. Use the proper special connectors.
The above points are partially guesswork as you didn't provided enough and detailed information on what cable you have, what the exact plugs on that cable are, what exact input sockets and what type of the sockets you have on your HiFi system, what exact output sockets and what type of the sockets you have on your soundcard, etc...
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