Would primarily be using the computer for coding, HTML, photo editing, design, and all that stuff. Used to play games on the PC (such as half-life), but have an Xbox360 for my gaming needs now, but may throw an okay graphics card just for movies and an average game.
Okay, time for some more specific recommendations, to put you out of your misery and confusion.
What is your budget?
"coding, HTML, design, movies"
These can be done on anything new.
"photo editing"
These can be done on anything new. If you do it for a living and work with super high resolutions (double digit megapixels?) then you may want a beefier CPU and more RAM to speed things up. Note that it won't be the difference between "can do" and "can't do," but the difference between "can do" and "can do faster."
"average game"
I think you need to toss out some more game titles. You mentioned
Half Life. If all you hope to play are some old titles like that, then you are probably fine with integrated graphics as they might be more powerful than the best graphics cards available when
Half Life first came out. That being said, if you have any hopes of playing even somewhat recent games in a pleasing manner then you need a dedicated graphics card and you can probably rule out a notebook computer.
Have you considered doing what some of us do, and have a desktop computer + a cheap notebook computer?
If you go this route, build yourself a new desktop now, and then buy the notebook later. "Later" means when you see a smoking hot deal, when you know you will be going on a trip and will need something portable, when you see a shiny new notebook computer and go "do want."
So, are you still using your "built a desktop computer 8-9 years ago" system today? If so, then ANYTHING current would be fine. Assuming you are using that ancient rig and knowing nothing of your budget, here is some generic parts choosing advice.
CPU - Core i3-2100 (or 2120 or whatever is on sale when you buy it) around $100-140
This is a super fast and power efficient dual core processor. It will probably run anything you need for the near future, and the socket 1155 platform it runs on is a current platform that still has future CPUs coming out for it, thus opening doors for upgrades (at least next couple years).
CPU cooler - just use stock cooler for now.
RAM - 8GB dual channel DDR3 memory kit around $20-50 depending on sales/rebates
DDR3 RAM is so stupid cheap these days that you may as well go 8GB. Heck, I just bought a spare set for $20 after $10 rebate. I used to argue against going 8GB on cheap gaming builds because nothing requires it, but at $20 it matches the going price of 4GB kits so, whatever. Just buy something that is at least 1333MHz (or faster, but not necessary) and something that is rated at 1.5v (or lower, but not higher).
Motherboard - something using the Z68 chipset that fits the case you choose $100-200
Most recent chipset for socket 1155 makes this a no-brainer even though there are cheaper chipsets. You likely won't notice much difference between cheap and expensive boards.
optical drive - whatever cheap SATA DVD writer $20
These are disposable. Useful for installing Windows/software and then it sits there doing nothing.
System drive - 120GB+ SATA 6Gbps SSD $120-220
SSDs are all the rage these days. All the cool kids use them instead of hard drives. A 120GB (or 128GB depending on brand/model) hits a nice capacity point being large enough for Windows and your software, plus even a couple games (as long as you uninstall what you no longer play). Also, it usually hits a nice performance point due to how an SSD works (smaller ones usually slower in some way). If budget allows, feel free to get something larger capacity.
Secondary drive - 1TB+ 7200RPM $130+
Alright, prices are lousy right now but it wasn't always so, and won't always be. Use this for installing your lesser played games on, plus storing all your data (especially your photos and other media).
Graphics card - for your uses probably anything lower mid-range in the $70-150 range will do, and will be so crazy fast compared to an 8-9 year old card that your mind will be sufficiently boggled. We can narrow this down once you throw out some game titles that you hope to play and what resolution your monitor is.
Power supply - anything good quality of sufficient wattage will do in the $30-80 range depending on the sale of the day or rebates. "Sufficient wattage" will depend on your ultimate graphics card choice. "Good quality" is a must, but you don't need "best quality." Basically, one that isn't "known to be crap." Let's get your graphics card chosen and we can tackle the PSU after that. Oh yeah, there is also form factor to choose, which will depend on what case you end up with.
Case - What do YOU want? Probably $50-150 should cover it. Do you value silence? Do you want it to be huge like you are making up for some personal deficiency? Do you want it tiny like you have Mac Mini envy? Do you want a black masterpiece? Do you want it white? Red? Do you want it to do double duty as a night light? Do you want to see the guts of your system? Do you want it to look super sleek? Super stealth jet fighter Pokemon I'm a 13 year old gamer? You want it to look like a Dell? An Alienware? What do YOU want? Oh crap, I think we've opened up a new can of worms here.
Operating system - Windows 7 Home Premium 64-bit $100
Most people won't need anything more than that. It runs all your software/games and supports 16GB RAM. What else do you need?
For a notebook computer, come back and ask about it WHEN you actually need to use one.