Question what is the best CPU upgrade for H-IG41-uATX?

Nov 24, 2019
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I have an old HP p6710t. Upgraded to: Samsung SSD, 4 GB RAM, E5800 processor. Don't want to spend too much on it, just get the max out of it. Tried an E 8600, it did not boot. (1 short, 1 long beep) I'm a little scared of QUAD core (95 W) or BIOS update (HP does not support any updates or help anyway)
What else can I try?? I heard that e5800 supports 8 GB RAM -is it true? Would it make a difference? (I don't play games)
Your help, advise, opinion would help a lot! Thanks!