Not everyone has the luxury of replacing their computers every few years, especially when what they have suits their purposes.
1. This is not a case of "every few years." This is A DECADE. This machine has not suited any modern purpose for years, and has been unsafe to use on the Internet for years. I'm not the bad guy here -- the OP was flatly irresponsible in not properly maintaining their machine over all this time, and is now paying the price for that.
This "kill it with fire" attitude is unnecessary and unhelpful.
2. You have grossly misinterpreted my response, and oversimplified it. It is both necessary to be truthful and realistic, and it helpful to disabuse the OP (and, apparently, you) of the ridiculous and fantastical belief that this problem can be magically fixed without spending any money. That attitude is precisely what got him into this mess in the first place, it is not going to get him out of it. Without that restriction, the fix for his machine (at least in the short-term), would have been simple: spend $20 on the Snow Leopard DVD and upgrade your OS, and he'll just have to accept the fact that some of his software will need to be upgraded, though very likely most of it will work fine, and the rest can be updated incrementally as affordable.
But placing a zero-money condition on any possible help is simply a limitation on any solution that makes the request impossible to take seriously, since the user has demonstrated that he is unserious about saving this machine and his data. Continuing to enable this unrealistic outlook will just result in further problems.
Contrary to your suggestions, there isn't a lot of software still supported for Mac OS 10.4, and finding any is difficult. And in many cases, expensive. While I did, as ONE of my suggestions, say that getting something newER would be the best option, the foremost thrust of my post was to point out the foolishness of the idea that this can be fixed for free. That attitude needed to be changed before any responsible, effective solutions could be offered.
There are some very real, in-the-field threats that prey on users like the OP who never upgrade anything. They work by exploiting flaws in older versions of the operating system. This is also why Windows PCs get so many viruses. I didn't suggest that his only option was to buy new machine; what I actually said was "with that attitude, there's not much you can do and so the best option is to just take it off-line." I continue to stand by that statement as the best advice under the limitations he placed on us and himself.
As I pointed out in my previous post, the OP intimated that he does not have a backup. If this is the case, there is NO WAY to make one without spending some money. In light of that, there is no solution – even free – that could be responsibly taken, since the risk of data loss at this point is so high, and with the age of this machine that has to be the first priority.
I'm well aware that budget can be an issue, but I don't go to my dentist and say things like "I ate too much sugar and now my teeth are falling out. I want you to fix it, but I can't afford to pay anything for any solutions you might offer!" I don't know about your dentist, but mine would just throw up his hands and move on to the next patient if I did that.
Once the OP decides to get serious about solving this problem, I have a wealth of suggestions for him that are low-cost, or free in some cases, practical, and do not involve buying a newer machine necessarily -- though that is still the best long-term option, and I think you are smart enough to know I'm correct on that point.
But I'm not going to waste my valuable volunteer time trying to help someone whose attitude precludes any meaningful help.