This is the memory limitation of a system running the 32-bit version of Microsoft Windows Operating Systems. Combined with the 32-BIT OS limitation, 4GB of physical memory installed will show approximately 3.5GB or less because Windows reserves some of the address space.

My new PNY memory modules have what looks to be a "cover" on them. Should I remove it?

No. These are heat spreaders and are designed to dissipate heat. They should not be removed.

I purchased some memory for my laptop or desktop and it is too big (or too small) to physically fit into the motherboard memory slots!

You have purchased the wrong memory for your computer. Memory is sold in both laptop/notebook and desktop formats. The part number for memory for laptops or notebooks always starts with "MN" and the part number for memory for desktops always starts with "MD".

I have purchased and installed memory but my computer is beeping or freezing when I boot up.

The wrong type (wrong speed or voltage) has been installed. Please refer to your computer or motherboard manufacturer for correct memory specifications.