Crash to desktop before first cutscene

Your PC doesn't meet the system requirements. The required MD Radeon HD 4870 is much more powerful than your Radeon HD 4350.

Ahh damn, I thought it might be. Would getting the game to run be a simple as replacing the graphics card? And would any low profile card fit/be powerful enough?

I'm fairly confident about the actual physical process of replacing the card, I don't trust myself to pick the right one though.

Recently, the availability of Gaming Quality GPU devices made in the Low Profile shape has gone down in the marketplace.  There never were a lot of good choices in that form factor, actually. 

Minimum choices are never really good enough, however, Newegg has this page for R7 250s, their introductory gaming adapter.  Is your Slimline able to run with the side panel off so you can use an R9 instead? 

http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&N=100007709%20600100181%20600038363&IsNodeId=1&bop=And&SrchInDesc=r7%20250&Page=1&PageSize=30

Something that Fred mentioned reminds me of this, also: many of the OEM "Slim" enclosures are NOT mATX standard, and thus, a problem often occurs matching the required PSU upgrade, such that replacing the actual case itself is often necessary to be able to use a standard mATX power supply. 

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@Chouxie wrote:

Ahh damn, I thought it might be. Would getting the game to run be a simple as replacing the graphics card? And would any low profile card fit/be powerful enough?

I'm fairly confident about the actual physical process of replacing the card, I don't trust myself to pick the right one though.

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You could just replace the graphics card, but you only have a 220W power supply. A better GPU will likely also require more power.

Good GPUs are usually two slots wide, which means your PCI-e slot should have a free empty space next to it. Usually that shouldn't be a problem, but with a pre-built HP desktop, it's a good idea to check.

As for hardware recommendations, I suggest you look at Logical Increments and pick a GPU and power supply of at least 'very good' quality for this game.

Also, to be perfectly honest, I would expect your current GPU to just run the game incredibly slowly instead of downright crashing it, so it may be possible that the issue may have a different underlying reason. (Unless someone could correct me on that. Could a slow GPU with the right shader and DirectX model actually crash a game?) However, you would without a doubt never get a playable experience with your current hardware.

Had a look inside, there's only one PCI-e slot, though it will run with the side panel off. From the cards I've been looking at it seems I would need a new 400w power supply as well, is that even worth doing? Or should I just forget about DA:I until I an afford a cheap(ish) gaming pc? I'm a student so my budget is not fantastic.

Sorry about any stupid questions/my awkward pc, I only got into pc gaming a couple years after I bought the thing.

In my own reply, I suggested the possibility of swapping cases to have access to a more standard form factor power supply.  The link is ONLY representative, being for what is called an "iTX" form factor mainboard.  Of course, I don't KNOW what what physical size the mainboard in your PC really is, but this so-called "cube" is on a rebate deal at $30: 

http://www.newegg.com/Product/Product.aspx?Item=N82E16811119299&cm_re=mATX_size_PC_cases-_-11-119-299-_-Product

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@Chouxie wrote:

Had a look inside, there's only one PCI-e slot, though it will run with the side panel off. From the cards I've been looking at it seems I would need a new 400w power supply as well, is that even worth doing? Or should I just forget about DA:I until I an afford a cheap(ish) gaming pc? I'm a student so my budget is not fantastic.

Sorry about any stupid questions/my awkward pc, I only got into pc gaming a couple years after I bought the thing.

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Technically, the cards involved absorb BACKPLANE spaces, also sometime referred to as slots as well, so that any adjacent "slot" has its space overshadowed by the "two slot" card that actually is only physically plugged into the one PCIe16 video interface.  Without illustrations, and I don't try that in this area, my explanation is only a ghost compared to a great deal more detailed articles that you can refer to on the internet. 

Generally speaking I really dislike the cases that the OEMs tend to use.  The link above is just to use for reference.