On my PC I currently have 2x8gb ram installed. My old PC had 2x4gb ram. Istill have slots left for two more 'peices of ram'. Will there be an issue with transferring the ram from my old PC to my new one?
There is a fair chance that the system will end up in a crash. Also are the specs(frequency, timing, voltage) same on both your new and old cards? If all the specs are same then only you can go for this combination of ram cards.
The timings have to match. It's best to use the same ram for all slots.
They do not "need to match" since latency parameters and clock are programmed into the DRAM ICs' memory control registers at boot-time by the BIOS. As long as the BIOS correctly determines the slowest common timings, it will make the DIMMs match by programming them to the correct same latencies as the slowest DIMM and use whatever the fastest clock is for the slowest DIMM. When the BIOS fails to correctly detect speed/timings, you can boot with only one pair installed, adjust timings manually and then install the other DIMMs.
As long as there are no electrical incompatibilities (which would mean at least one of the DIMMs is not compliant with the JEDEC spec), it will work.
Did you reset the CMOS to force the BIOS to re-detect RAM and try manually entering the slowest common timings and clocks in BIOS to rule out timing misconfiguration?
If you have no idea how slow your slowest DIMMs might be, you can try manually configuring the BIOS for 1066-9-9-9 (about the slowest DDR3 you can get) and see if that works. You can also try the same thing with your old PC to see whether this might be a problem between the DIMMs or a problem with the PC.
If none of the above worked then you likely are the unlucky owner of at least one pair of DIMMs that are out of JEDEC spec.