Honestly, a pre built PC is a terrible start for a gaming PC. The best recommendation would be a new case, new motherboard (most pre builts come with cheap ones). Salvage the RAM (but replace it in the future for a higher clocked high performance one), HDDs and buy the rest. Forget about upgrading the older machine.
If it isn't in your budget, I recommend to delay the parts and wait to be able to start a new build from scratch. You are saying that a laptop is out of your budget, so a gaming PC is probably WAY out of your budget. What GPU are you thinking about?








