I had a good look at the Linode site. It looks good. You get a virtual server. I could basically duplicate what I am doing at home, but in a limited form.
I could start at the bottom level, what they call a Linode 512. You get 512 meg RAM, 20 gig disk space, and 200 gig of download traffic. That costs $20 a month. It looks pretty limited, but you can start with that and see if it suits your needs. If you need more RAM or disk space or network traffic, you can add on extras, or move up to higher base levels.
My web and mail needs are small. I checked the amount of hard disk I am using, and 20 gig will fit it. Most probably I could fit into 512 meg RAM too. And I would have no problems at all going under 200 gig of traffic.
Best of all, one of the Linux distributions they offer is Slackware 13.37. They have good forums, and plenty of good documentation for setting up.
They have a backup service. At the lowest level that costs an extra $5 a month.
So if I went ahead with this, I would have a virtual server "out there". Not subject to the same hardware irritations that I just experienced. Obviously you can't do away with the hardware entirely, but I don't have to manage the hardware. I just have my little virtual world, and I hopefully exist outside of hardware issues. I don't have to worry about a pizza driver around the corner slamming into the power transformers and leaving us without electricity for a day and a half, which happened here a few months ago. I don't have to worry about network outages. If we lose the network, or we lose power, the websites would still get served up, and mail would still be accepted. I see a lot of pluses in this arrangement, and no real minuses.
I did a lot of reading about Linode. There are a lot of blogs and a lot of results of Google searches. Practically all of it is positive. Okay, I am sold. Where do I sign up?