It's around a year old+ and hasn't been used in months because it got too slow. I managed to put disk optimizer on and it's taken at least 3 full days to reach 85% analyzed and anything else takes a long time to load and frequently stops responding for a time
What's the best solution to make it run faster ideally with out losing any installed programs/data that's on it
The best thing, IMO would be to install an SSD. Solid State drives are significantly faster than hard drive and will improve overall system responsiveness. The only problem is that SSDs are more expensive per gigabyte currently (prices are always falling). You can clone your HDD to an SSD using cloning software. SSDs generally include a free code for cloning software like Acronis True Image or something similar.
I would also recommend upgrading RAM. It has 4 GB of RAM which isn't a lot by today's standards. I would go for 8 GB of RAM.
The other thing that will most likely help a lot would be to get rid of the OEM bloatware. OEMs like HP, Lenovo, Asus like to include a bunch of useless programs to "enhance" your experience. In reality, they do the exact opposite. These programs may include: Diagnostics programs, telemetry programs, "helper" programs, product experience survey programs,"productivity" programs, etc. The majority of these programs are beyond useless and just slow things down. Whenever I setup a new system for family or friends, I always offer to uninstall these programs.
I have heard that windows 10 can install a fresh versions of the windows 10 operating system on top of the old one without effecting any of the documents or programs that is currently on it, sorry you will have to research yourself on how to do this as I'm still only using windows 7
you should have mentiond the computers specs because if it doesn't have enough RAM memory on it then that is something you would have to get upgraded