Hi, CalenteDama.
I did some checking on your system and, sorry to say, it's not designed to run demanding games like The Sims 3. The issue is two-fold and is already something you said you wouldn't consider. However, let me explain why you're likely getting the black screens. Apologies as this can get technical, but I will try to keep it as simple as possible.
The setup you have for graphics is similar to the setup that's in my current laptop (which also won't run The Sims 3 that well). It has an integrated graphics chip on the processor (the AMD Radeon HD 7560D) paired with an r5 235 card with 1 GB of dedicated video memory. The two graphic chips are designed to run in tandem in a setup known as Crossfire. The problem is, neither graphics card is all that good.
Leaving aside the on-chip graphics card, let's talk about the r5 235 card. On first glance, it doesn't look too bad. It has decent clock speed and 1 GB of memory. Base game for The Sims 3 only requires 128 MB of memory, so it should be plenty. Dig a little deeper, however, and the issues start to show. For one thing, the memory used on this card is DDR3, which is the slowest memory for a graphics card. This is important as slower memory means it takes longer to render the next screen which causes the game to stutter.
Another issue is the memory bandwidth (aka memory architecture), or how many pieces of information can be sent and received at a single time. Also known as the bit rating. Most mid-range and even some high range video cards use a 128-bit memory architecture. The r5 235 uses a 64-bit memory architecture. It has to work twice as hard to push out the same results. It generates more heat as a result, which the system's cooling apparatus has to try and remove.
The reason people are suggesting a new graphics card and power supply are two fold. One, a mid-range graphics card will play the game well at mid to high settings for an outlay of roughly $100 - $130 USD (cheaper on sales). But any modern graphics card in the mid - high range will require a special power connector and a little more power. Desktop systems by HP, Dell, etc. are notorious for not including these connectors and for installing power supplies that just cover what is used by their configuration.
So, if you're dead set against a new graphics card and power supply (and I completely understand not wanting to spend more money on a brand new system), I would recommend you lower the settings in The Sims 3 to help alleviate some of the issues. In this case, I would especially recommend turning off Advanced rendering, setting the detailed lots to 1 and putting all other sliders at medium settings. Also, if you are running the game at 1920 x 1080, lower the resolution to 1366 x 768 or 1280 x 720 and see if that improves the game and stops the black screen.
Hope this helps and happy Simming!
Flynn
