I've inherited a 12 year old PowerSpec desktop.?

PowerSpec is a MicroCenter brand. More ram won't help. You will not get good performance out of a 12 year old system, but to discuss the subject, you need to list all the parts.

It's running. Speccy and Belarc identify most parts. If the power supply has a label, what can you tell us about brand+model?

https://www.ccleaner.com/speccy

https://www.belarc.com/products_belarc_advisor

CCleaner to clear temporary cache and use a registry clean.

https://www.ccleaner.com/ccleaner

CPU, CPU Cooler, Motherboard, ram, Storage, Video/graphics Card or processor, computer Case, Power Supply, Optical Drive (dvdrw), Operating System, Monitor, sound Cards, Wired Network Adapters, Wireless Network Adapters, Headphones, Keyboards, Mice, Speakers

A 12 year old PC is prior to Intel 1st generation core i, introduced in 2010.

Your top end may be a Intel Core 2 Quad Q6700 in a Socket 775 motherboard.

The PC is worth less than $100 pretty much.

CPU info site:

http://www.cpu-world.com/CPUs/Core_2/Intel-Core%20...

CPU speed site:

https://www.cpubenchmark.net/cpu_list.php

CPU speed, at best is 3277 score.

Depending upon the motherboard, you may be able to buy and install a used cpu in line with these old ones. You cannot use new CPUs.

You might clone and swap the HDD for SSD.

First determine what you have to discuss it.

Storage size and amount of ram says little.

   Hi. Your best option for it is to remove Win7 again & re-install the 32bit version, it will also allow the 32bit software on it to run faster under the correct Win core.

   And if You want to use it online, download a live bootable linux distro or run 1 from a flashdrive installation whenever You connect.

   The 500Gb & 4Gbs RAM are fine for Win7, all versions. use the tricks foubnd online to customize things like virtual memory, performance themes & non-super-fancy add-ons.

   https://www.youtube.com/results?search_query=optim...

   Do NOT use 3rd-party apps for customizations, they're all designed for different systems & different Users, & none end up working right. You're better off taking the 15 minutes to learn what they do automatically so You can tweak it just right.

            G'Luck!!!

Doubtful. better to just get a newer computer

RAM may be damaged. If it's just one stick, replace it with another one. I also recommend replacing the hard disk. You could use a cheap SSD for it instead, even at half the capacity and still be useful. I would be more comfortable running XP (32bit) on it since it's that old.

No, more RAM will most likely not help it. Your main bottleneck is your CPU (since we're talking about a 12 year old PC here). You need to find the specs for it, and figure out its clock rate and cache memory. The second biggest bottleneck is your HDD. If your CPU is very weak (only 2 cores 2 threads, or 2 cores 4 threads || very low clock rate like 1.8 GHz or something around that), then you won't get a performance boost no matter how much you try. Adding RAM to it certainly won't help it either. You'll find little to no difference. If that's the case, then the PC is pretty much useless. You'd be best off using Windows XP (even though it can only see 3 GB of your total 4GB), but you want something to work with. 

IF, on the other hand, you have a good CPU and a considerable clock rate (not gaming level, but still), then upgrade your HDD to an SSD. If this isn't going to be your main system, then go for something cheap. A KingDian S280 480GB would do the work just fine, and you'll have considerable performance boost. Nothing too interesting, but usable for web browsing, and using some software applications that do not require graphical rendering. If this is going to be your main system, however (which is completely ill advised, mind you), then go for something like a Samsung 860 EVO 500GB 

If it will actually support more RAM. If it's 12 years old you probably have PC 6400 ram. And the hard drive is pretty darn old so if you want it to be faster put yourself a solid state drive into it and get yourself some ram off of eBay. Before you do this however run crucial memory scan off of the internet it'll tell you how much RAM that you can actually put into your computer if your computer can only do 4 gigs of RAM it's not worth you purchasing a solid state drive. Just use Linux mint on it. It'll be faster than Windows 7.

what processor? the CPU makes the biggest impact on speed.

if it is a Celeron, Sempron or Turion, ditch it.

if it isn't one of those, consider switching to an SSD drive for a slight boost in response times.