mobo diode light not light on (always on if working), psu fan still working. my guess is failed mobo.
integrated graphic save space if going mini or micro casing
Hard to say, PSU with voltage regulation/supply issues will also be able to light up your rig, spin the fans but just cannot power on the rig.
CPU+ Mobo: MSI FM2 A88XM-E45 + A10-6800K (314)
RAM: 2X G.SKILL PC 12800/1600MHZ DDR3 CL11 VALUE RAM (4GB) (100)
PSU: FSP 450W 80+ HEXA PLUS (58)
Case: CM N200 (55)
Total cost: $527
Buy at PC Themes, #04-15, and ask for discounts. DIY yourself. If you can't into DIY, get PC Themes to assemble for you for a fee.
Notes:
1) You want the strongest iGPU in the market, so the AMD A10-6800K is chosen as the A10-7850K is just a slightly more power efficient CPU without any major increases in performance. The iGPU in the A10-6800K is about roughly equivalent to a R7 250 GPU (DDR3 VRAM version) and thus should be packing quite a lot of (integrated) graphics power for your games.
Also, if feeling adventurous, both the CPU and the iGPU can also be overclocked for better performance. Do remember to buy a aftermarket CPU cooler if doing OC though.
2) The MSI FM2 A88XM-E45 is chosen as it is a socket FM2+ mobo and thus is compatible with both FM2 CPUs (the A10-6800K being one) and FM2+ CPUs. This means that in the future, you can get an upgrade simply by updating the mobo BIOS and inserting a new FM2+ CPU, no need for a new mobo, save lots of $$$.
3) 2X sticks of 4GB DDR3 RAMs are used as AMD APUs require the presence of at least RAMs in a dual-channel configuration for good graphics performance.