Hi Astrovel and welcome to LQ!
Regarding the older computer, the system specs might be helpful here for people to offer some advice. There are distributions which work well with less RAM and older hardware. Usually things like the video and network are the biggest hassles, but also the largest impacts to user experience. Many times I've found that distributions which have been around for a while tend to have older versions which work well with older computers. For instance if the computer is circa 2009 and you find a release of Linux which was about 2010-2011, there's a good chance it may work. I feel that is the idea with the Ubuntu 7.10 version they have suggested. I do hope that this person is not repeatedly charging you either. Things like ISO files which you can write to a CD, DVD, or USB thumb stick are all available from the web and it turns out that you need to do a little bit of research to learn how to make a boot capable media from the ISO files and also a little bit of research to know what ISO files you may wish to download. Please consider that if you happen to be, being asked to continually re-invest more money to a third party.
You are on the right track, trying live distributions on that system to see what can work.
On the Dell Inspiron 3847, I feel you may benefit by learning how to disable Safe Boot. I would recommend you perform a web search with the terms, "dell inspiron 3847 disable safe boot install linux", or instead of "safe" use "secure". There seemed to be tons of solutions and rather than myself say "here, use this one", I feel you should evaluate those, read them a bit and choose the one which follows your boot scheme.
Best of luck. Please update with the specs of that older machine and let us know how things are going with the Dell.