Incompatible GPU or broken computer??

Bit of a long-winded story so apologies in advance but here we go!

Recently decided to upgrade my GPU in my Dell Inspiron 620, and looked on here for compatible cards, decided to go with the Radeon HD 6450. Very new at GPU upgrading so didn't realise there's different versions of cards by different manufacturers, so I went on eBay and bought pretty much the first HD 6450 I saw, and left it at that. (it was listed as a "1gb ATI AMD Radeon HD 6450 PCI-E Graphics card, Dell p/n 0WH7F" but more on that later)

Card arrived, (the bracket was too small, most likely for a small form factor PC but I didn't think too much of it as I could still insert it) I did everything by the book, including disabling Intel HD Graphics in the device manager, slotted it in firmly, booted up the computer and..nothing. No BIOS, no beeps no nothing, the only thing working was the fans, including the one on the new GPU.

Tried a bunch of different things as suggested by other people having similar issues with similar cards but to no avail. Tried it in my dad's PC (not sure of specs right now, but it was a build from pcspecialists, I know it's got a better CPU than mine) and it worked INSTANTLY.

I thought it could be the PSU not outputting properly so I swapped out my Inspiron's 300w for dad's more powerful 450w one, but still the same problem, however without the card my PC still booted normally with the new PSU. The only thing left to test was the PCI slot but unfortunately I have no other cards to plug into it, but I suppose if it runs the fan that's a good sign?

My dad's PC seemed to recognise it as a Radeon HD 7000 series though, and when i did a test at userbenchmark, it confirmed it as a Radeon HD 7470, rather than a HD 6450, and a quick google search confirmed that is exactly what I've been incorrectly sent. (https://www.amazon.co.uk/radeon-profile-display-desktop-computer/dp/B00CR230G)

SO MY QUESTION

Is it plausible that this weird tiny-bracketed obscure Radeon HD 7470 is just incompatible with my Inspiron? Or is my computer broke?

After all, I've only seen about 3 GPU's officially listed by Dell as compatible the 620..

I have now ordered a proper official looking Radeon HD 6670 by ASUS (which I'm told is a much better card in the first place) so I suppose I'll have to wait and see if that works, but while I wait, does anyone have any ideas re: this weird video card I was incorrectly sent? I've let my dad have it, it seems to work great for him..

1gb ATI AMD Radeon HD 6450 PCI-E Graphics card, Dell p/n 0WH7F