Programmable Interrupt Controller is a controller that (roughly) controls communication lines between the processor and the various hardware parts of the system (disks and storage units, graphics card, various other cards like sound, network adapters, game ports, keyboard, mouse ... ).
It is normally integrated within the processor, since the early Pentium chips. But, at the time systems were much simpler than today. The use of systems with more than 1 processors and many I/O channels needed a better coordination. It seems that the ACPI makes the system running faster. ACPI can be handled by win2000 and xp, but not by older ms systems, like 98, 95 or msdos. So, with newer systems ACPI is to be enabled.
With Linux, we need sometimes to disable ACPI for various reasons related to the specific kernel parameters. In an installed system, we can do it with some boot parameters in the boot configuration file.
In your case, you need to run Linux just as the support system to run Gparted (I understand that your usual system is windows and you just want to resize a partition). So, you can try to disable this ACPI BIOS feature to see if the Linux system will boot and work. This change is reversible, so you have to undo it after resizing and testing.
Can you, please, give me your BIOS type and version?
*** It is highly recommended to backup any important files before doing resize/move operations. ***