Unfortunately, no, those don't do much good for our case. It's only displaying various successful events and errors that occurred.
Bottom line is this, your system has quite the history, and crash dumps aren't being generated. We cannot manage to do administrative tasks (likely do to malware messing w/ various administrative features, and corruption in general), so we cannot get said dumps to generate. Best case, we can get dumps to generate, but your system still has all of this history and it's very difficult to troubleshoot around all of the hoops we'd need to jump through. What's likely occurred here is just a large amount of system/registry corruption and issues from malware over time, and overall OS age.
The best thing to do is use an external drive if you have access to such (or even a thumb drive with enough space), to go ahead and back up any important documents (files, pictures, etc). No programs, because they've likely been thrashed. We'd want all programs fresh with a clean install, nothing left over. When we do this, we start on a brand new slate, and if you crash at that point, we can very easily take the appropriate steps because we know your OS isn't in complete shambles because it's a clean install.
As far as not being able to locate your install media, do you have a recovery partition on the system? If so, give that a try. If not, perhaps a friend has an install CD you can borrow? Worst case, you'll have to contact the manufacturer and have them send you recovery media.