The Inspiron 530s (slimline)/ 530 has a FoxConn G33m02 motherboard made to Dell's specifications and will support (as far as I know) the following Socket LGA 775 processors:
Intel Celeron processor 430
Intel Celeron Processor 420 (1.6 GHz, 800 FSB)
Intel Pentium Dual-Core 2140 (1.6 GHz, 800 MHz FSB)
Intel Pentium Dual-Core 2160 (1.8 GHz, 800 MHz FSB)
Intel Pentium Dual-Core E5200(2.5 GHz, 800 MHz FSB)
Intel Pentium E6500 2.93 GHz dual core processor
Intel Core 2 Duo E4300 (1.8 GHz, 800 MHz FSB)
Intel Core 2 Duo E4400 (2.0 GHz, 800 MHz FSB)
Intel Core 2 Duo E6320 (1.86 GHz, 1066 MHz FSB)
Intel Core 2 Duo E6420 (2.13 GHz, 1066 MHz FSB)
Intel Core 2 Duo E6550 (2.33 GHz, 1333 MHz FSB)
Intel Core 2 Duo E6750 (2.66 GHz, 1333 MHz FSB)
Intel Core 2 Duo E7300 (2.66 GHz, 1066 MHz FSB)
Intel Core 2 Duo E7400 (2.80 GHz, 1066 MHz FSB)
Wolfdale Core 2 Duo, E8400, 3.0GHz, 6MB, 1333FSB, 65W, E0
Wolfdale Core 2 Duo, E8500, 3.16GHz, 6MB, 1333FSB, 65W, C0
Wolfdale Core 2 Duo E8500 (3.16 GHz, 1333 MHz FSB)
Wolfdale Dual Core Kit, E8600, 3.33GHz, 6MB, 1333FSB, 65W, E0
You can use the same/default heatsink/fan and the 250w PSU
Remember new thermal compound.
Prior to installing the processor you need to check that you have BIOS Version 1.0.15, or higher, so it should work for you. But I would be more comfortably with the latest bios.
Are you running 32 bit windows, then this is probably your problem. Run windows 7 x64 or newer (I`ll still in win7 x64, because win8 and win10 is garbage
Does the Dell logo show up when you boot, and does it say only Inspiron under the logo? There are four different 530: 530, 530a, 530b, 530c (I don't know the difference, but some of them can run quad-core cpus,
but only if you have the G33M03 mainboard and 350w PSU.