Hello Dave,
Sorry about the late response, I had to go to a a shop to have them connect the computer to an outside/another line. Unfortunately my friend's connection that I had planned on using to test my system had a USB port on his connection switch and I was afraid to connect to his line for fear of transferring a virus to his system if that port was read/write-able.
The shop said they had no trouble connecting to the websites I mentioned to them (REI and Campmor). The shop also ran a virus checker too and found nothing.
I brought the computer home and hooked it up and I have the same problems (slow connection, no connection,or partial connection to websites and poor/scrambled picture quality). One exception is that the Campmor site for some reason is showing all the pictures correctly at this time but still has that skull icon in the middle of a rotating disk (looks bad and is also on my wife's system) when I hit the "Show Next Results" button to go from one page of merchandise to another (I'm pretty sure the skull icon was not there before these problems started). Do you find that icon on your system (white skull inside a green disk)?
I think I either have some connection problem at my home as you suggest, a malware problem, or a corrupted Microsoft XP OS. I could buy a new cable or connect my cable to my wife's computer if you think that might help (see next paragraph); I already tried moving the cable from port to port on the Internet switch located next to my wife's computer in another room without a change in performance. Or I can purchase a CD with Microsoft XP for about $30, wipe my system clean, and reinstall the XP (the shop did not recommend updating to Windows 7 because I have marginally enough RAM).
Because the other computer in my home does not have any issues connecting to websites (though it does take awhile to connect--she has noticed lower performance since going to Windows 7 and then 10 OS), I assume the Internet connection in my home is not faulty. It's possible the cable running from my computer to the Internet switch in the other room is faulty (about 40 feet long, goes under some doors [possibly stepped on though I have protective covers], up walls, and on the ceiling).
I primarily use the computer for e-mail, word processing, and a little shopping. It's getting hard for me to justify purchasing newer equipment when my needs are so small. I even considered converting to the Linux OS system but I don't know if I'm technically skilled enough to install and operate that system. Also, I have considered going to our city library to use their computer from now on; I'm fairly active on e-mail with committees and the library option would not be ideal.
Since my wife's system is going strong and is updated, I'm not looking at a hand-me-down from her anytime soon either; we have done this in the past and we do try to keep our machines as long as possible and recycle them when we upgrade in this way. We are concerned about how these machines are recycled in foreign countries and how their workmen may be exposed to toxins; so we keep our machines as long as possible.
Any further help and suggestions would be appreciated and I appreciate all the help you have provided to date. I'm stumped on what to do next.