What version of PCLOS have you installed? I did not see it above ... maybe missed it.
Just FYI I installed LXDE Full (new version) on an old Dell P4 single core with 4MB nvoard graphics ana a total of only 256MB RAM. Dang thing installed in about 6 mins!
Anyway, I can Suspend to ram, and pressing the on/off button on the front of the machine brings it right back up.
I also just now tried Hibernate - Suspend to disk - and it saved to disc.
Switching back on restarted the OS but it picked up the saned session from the Swap partition and came up properly.
In both cases I had Clemtine playing some music when I selected to suspend ...... and in both cases Clemtine picked right up where it had left off, continuing to play as if nothing had happened. I did not have to tell Clemtine to play after resuming ..... it just continued from where it stopped. I was quite impressed.
All of the above is by way of explanation only, but it does make me wonder
1. if you have inspected the CPU/Heatsik to ensure there is no dust in there and that the thermal paste is intact or not dried out.
2. After that I would be suggesting maybe a parallel install on a small partition of LXDE .... it is light on resources.
3. How much Swap space do you have?
With 3GB of RAM you could need up to >6GB of contiguous Swap space to successfully Swap to disk.