Help upgrading Prebuilt HP!

[Firestar1161]

I've done lots of reading over this, with only a few questions unanswered. Firstly stated, I have an incredibly small budget, so small that I will not even post a number. I know this is not conductive to upgrading a PC, but I understand that. My goal here is simply for a really low quality build that can play some newer games. Stated again; I'm NOT expecting to run Skyrim at 1080p max settings. My main goal is to upgrade the CPU slightly and put in a graphics card, while slipping in a new PSU to power it.

I have the CPU selected, and while this is incredibly low par, it's already 2x better than my current CPU, which runs most games that I'm wanting.
PassMark - Intel Core2 Duo E8300 @ 2.83GHz - Price performance comparison

Here is my CURRENT CPU: PassMark - Intel Pentium E5300 @ 2.60GHz - Price performance comparison
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The graphics card will be decided after everything else is said and done, and the budget is slightly flexible. The CPU I've picked out is available to me for $25, and I can probably go 30 or so on the PSU.

I understand that people here will advocate for me changing the Mobo, or getting a new PC, etc. Please understand I'm going to college, have almost no money, and just want something that can play a few games on low settings in my downtime.

To further why I want to upgrade this, this was my Mom's PC [ She is no longer with us ] ( I've kept her going for nearly 6 years ) and I think with budget leftover I'll upgrade RAM from 6gb to 8.

Here is the model of my computer: http://h10025.www1.hp.com/ewfrf/wc/document?cc=us&lc=en...

Here is the model of my Mobo: http://h10025.www1.hp.com/ewfrf/wc/document?cc=us&lc=en...

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So the CPU uses the same Wattage, and the card I've been looking at is a Radeon HD 6670. Is there any way to know if a stock ( Not sure if 80 plus certified ) 250W can power this card, and are these upgrades adequate?

 

[Firestar1161]

Nevermind, did some searching, the requirments are a 400+W PSU. So I'm in the market for a new PSU as well... Great.

---------- Post added at 02:02 AM ---------- Previous post was at 01:58 AM ----------

Do you guys think a PSU will fit in the case my model is? Rosewill 450W Desktop PC Power Supply Unit PSU Model PS 450W Fully Tested | eBay

 

[BK_123]

If you didn't know what CPU's your mobo supported then I found this on the link to the computer you have.

Motherboard supports the following processor upgrades: Intel Core 2 Quad (Y) Q9xxxx
Intel Core 2 Duo (W) E8xxx
Intel Core 2 Quad (K) up to Q6600
Core 2 Duo E6x00 (C) up to E6700
Core 2 Duo E4x00 (C) up to E4400

 

[Firestar1161]

Oh yes, I know which CPU I'm getting, and the mobo supports it. I've slowly worked down all things... Now I need to know if that PSU is adequate for the 6670 Radeon. Or maybe I don't need a new PSU at all?

---------- Post added at 02:49 AM ---------- Previous post was at 02:48 AM ----------

In response to your list of processor upgrades, I've checked that list It's a Core 2 Wolfdale E8300, which falls in the line of support. My main issue is questioning of the PSU now.