The 7300LE draws 5 watts more than a HD5450. Chances are the PSU is not the cause of your BSOD problems. You did uninstall the old nVidia drivers and installed the correct AMD drivers for the HD5450 right?
Have you updated your OS?
Have you uninstalled all the crapware that Dell bundles with their PCs (this is one of the main causes of slowness and errors on Dells)? I usually reccomend a clean install of windows on any Dell due to these issues.
Is your registry in good order? Have you ever reinstalled your OS since the PC was new?
Even under the best circumstances that computer is never going to be fast it is simply too outdated. But it should run without BSODs and be able to handle basic tasks such as office applications, web browsing, video playing, and light photo editing. The HD5450 should help graphics slightly but it is not a gaming card, it's primary benefit is DX11 support although if you still have XP that doesn't matter much