Some suggestions would be the low profile HD 5450, HD 6450, HD 5570, HD 6570 or GT 430. Also, make sure they come with low profile brackets. According to your specs, the card must be within these dims so check carefully:
1 low-profile PCIe x16 graphics-(H: 2.5" X L: 6.6")
We have several Optiplex 755's in our office and have found no issues with them playing Video on XP or 7.
Some of these have the Radeon HD 2400 card which was customisable for the system. We also have a couple of Optiplex 745s and they are running Windows 7 perfectly with onboard graphics.
On 64 bit Windows 7 what drivers are you using? You should have:
• Dell System Software R282538
• Chipset R302424* (or R174616 if it doesn't work)
• Chipset Sol R286630* (or R255438 if it doesn't work)
• Chipset HECI R253211
• Intel Video R240415
• Network R162323 and R173716
• Audio R164900
* Drivers from Optiplex 760 - Windows 7 drivers will probably work with the 755. I can't remember what one of the 2 I used so I put them both there.The machine works perfectly with that driver set.
Windows Reinstallation Guide and Related Wikies See here for other wikies such as Customising and Using Windows 8.1, Dell Wireless Cards and Unofficial Drivers.
You might have any faulty hardware in your system. I also have an Optiplex 755 running in the same specs though I have HDD instead, but SSD is much faster.
Who wouldn't want a piece of something, eh?
The onboard video will only run Hardware Accelerated Graphics with XP. If you insist on using windows 7 you need a real GPU aka Video card.
An Inexpensive Radeon 5450 would work fine.
Current Versions of Flash REQUIRE a GPU
This document lists the GPUs chipsets and graphics drivers not supported by the Stage3D feature introduced in Flash Player 11 (desktop) and AIR 3 (desktop). In such a scenario, your content still runs, but Flash Player 11 and AIR 3 will fallback to software rendering.
Note that using the Stage3D APIs ensures you that even when using software rendering, your content should perform significantly faster (around 10x in some cases) than with previous versions of the Flash Player or Adobe AIR.
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The 6450 is newer, more powerful and about the same price.