I just had my daughters laptop (same model) fixed due to having this same issue. The Tech explained he reflowed the video chip. He stated the laptop should always be used on a flat surface. If at any point the internal cooling fan is smothered, this causes the area to warm and slowly soften the solder and eventually cause the video chip to disconnect. He also stated that he has repaired lots of dell M5010's due to this same issue and declared that it is a manufacturers defect. Until Dell does a recall, above is how the laptop can be fixed. With the laptop now working, the Tech strongly advised me to get a cooling fan for added cooling power and stated to always use the laptop on a flat surface. I purchased a "Targus Space Saving Lap Chill Mat" ($35) which has two cooling fans along with a platform that can be raised or lowered. I love this mat! The cost of the repair was $100. Hope this helps.
See this link for Alienware beep code table - this table should be applicable even for your inspiron / any other Dell PC. Looks like the processor is faulty. Contact Dell Technical Support if you have warranty for your PC.
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