Help with pc hardware

Hello , so my laptop broke down recently and i want use an old computer to play league, but the fps drops are massive . Its a weak computer but i want to buy a part that is going to run league smooth. I know this are sheit components , but can anyone tell me witch one of these should i replace. Keep in mind i need cheap as it gets option. Ati radeon HD 4600 graphics card AMD athlon 3800+ 2.4ghz processor and i have 4 gb ram witch should be enough all drivers are up to date. so should i replace both graphics card and processor or just one of them. thanks.
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