Game's performance depends on countless factors. Showing what you have under the hood of your PC can only help to determine whether or not you meet minimum requirements (in theory), that's it.
First of all, why do you (both of you, guys) have an x64 system installed when you have only 4GBs of RAM? You waste space to install unnecessary x64 libraries you don't even use. That may impact your performance, to a degree. It's low end hardware for today's standards, so if you want to use it for more demanding tasks (that includes gaming), you need to learn how to make the best use of limited resources you have. Oh, and inb4 "x64 allows you to install more RAM" - yeah, that's correct, but there's no reason to do so, simply because RAM all alone won't help you much when you don't have powerful enough GPU and only okayish CPU.
Also, speaking of hardware, noteboooks don't age well. Due to the fact they're ightly squeezed, they tend to have problems with overheating after few years, if you don't take care of them, like checking their temperatures once a while and taking proper counter measures if they're high (cleaning dust, changing thermal paste, and taking care of the OS, which I'll talk about later). Older hardware will perform significantly worse than new one - and judging by your specs, I suppose your notebook is now brand new.
Second of all, you didn't tell what are your GTA IV graphical settings. If you can switch something from medium to low, experiment with it and find a combination that works well for you. Shading, reflections and anti aliasing are often overlooked. As mentioned before, commandline.txt may also help if everything else fail - Google it.
Third of all, if you haven't installed official patches, do it. First 4 optimize the game, the rest focused on multiplayer features if I remember. If you own a digital copy of GTA IV, it should already be nicely patched.
Now, software issues. You have an x64 system installed, despite your hardware not being capable of making use of it. On top of that, however, there's tons of little things related to system which impact its performance - most important being amount of trash your PC created throughout the years. If you don't use CCleaner or similar program (like Advanced System Care, etc.) on regular basis, it's a good time to change your habits. Clean the junk and registry - you immediately should notice a difference.
Next step, defragment your HDD, for instance with Smart Defrag, or any other program of your preference. Organized data equals quicker access to your files. Also, make sure you have some free disk space on your partitions. Don't fill them up to the point you can't squeeze anything more.
Doing an anti-virus scan won't hurt either, although it may be time consuming.
Don't forget to update your drivers - another often overlooked thing. If you don't know how, download an automatic manager, like Driver Booster. It's easy to use, you shouldn't have any problems.
Last quick tip, close unnecessary processes working in the background. Disable your anti-virus real time protection before launching GTA IV, close down your browser, torrent downloader, everything. The less memory you use the better.
I could elaborate on optimization and computer health forever, but I think I've mentioned most important issues you should look up. There's more you can do, of course, but for now I believe that should be more than enough. Good luck - take care of your computer and it'll do what you want, in margin of reason.