(tl;dr/short version at the very bottom!)
If you send me a PS2 memorycard of yours via mail, I can mod it for you to allow you to run homebrew on your PS2.

Allow me to explain how PS2 'softmodding' works;
When your PS2 boots up, one of the first things it does is check the memorycard in Slot1 for a specific set of 'apps' for it to run. This is normally for PS2 updates, I believe.
However, you can put your own applications on it for the PS2 to run.
The app most people use is a simple loader. It 'replaces' your PS2s System Menu with a homebrew launcher. Similar to the Homebrew Channel on the Wii (Though a little less polished ).
Keep in mind, none of the changes are permanent. Reset your PS2 with the modded memorycard not in it, your PS2 will be 'unmodded' again. So everything you load is based off the Memorycard and not in the PS2 itself. So it's virtually harmless.

Normally, to get the application in your Memorycard in the first place, you need to either have a PS2 'gameshark' of some kind, or you need to take your PS2 apart, force the laser to run at specific moments, swap out discs of very specific games at very specific moments.
So modding your PS2 without any help or tools is 'alot' harder and stressful than modding say, a Wii or PSP.
I personally did the later. I spent $30 on a 007 game just to mod my PS2. The 'plate' in front of the CD drive is now ruined due to a mistake. T~T.
In any case. If you have the application on a memorycard already(like I do), transferring the application to another memorycard is 'extremely' easy. All you have to do is copy it to another memorycard just like you would any normal PS2 game save, because it can be moved, copied, or managed though the normal PS2 'save manager' menu.



All of that said, if anyone wants their PS2 modded, let me know. As long as you pay for the shipping to get it here and send it back(I live in Oregon), I would be willing to mod anyones memorycard completely free of charge.
And yes, you can still use the memorycard like normal once it's modded. Though some homebrews might use the memorycard to save data too, like settings(Though those homebrews usually have a setting somewhere for 'save to USB instead of Memorycard').

When you download other 'applications' to use, you normally put them on a USB Stick to load them up using the Memorycard loader(Sounds more complicated than it is, I promise!). You can however put applications you want to keep on the memorycard anyway, but it's usually just a waste of space.
PS2 modding enables the use of Emulators, though I never used any of them myself, so I can't vouch for how good or bad they are.
It also allows you to play PS2 backups off a USB stick, or a Burnt DVD/CD.
Fair warning though, playing off a USB stick is a tad complicated and a little annoying. For example, you need to get the .iso/.bin(Or whatever else) and convert it to a specific format for it to be loaded. Not too much of a hassle, but it's easy to forget.
In most cases, loading off USB is also a tad slower. So in some games, you might experience longer loading screens (Not too much longer from what I've noticed though).
Also when using a USB stick, some games might bug out. However, in my experience, if the game runs, it runs fine. Which I think the PS2 loaders have like ~%80 compatibility or something, so normally it shouldn't be a problem.Games I've tried on the loaders:

Shadow of the Colossus (And beat it using the loader), Grafetti Kingdom(Also beat it using the loader), and RPGMaker 2 and 3.

There are also two different loaders, I believe. So if one loader doesn't work, the other usually will.


Also, if you have a phat PS2 and a harddrive, you can put games on the HD and play them as well. Though I've not done this, so I can't vouch for speed or bugginess. To get a game on the harddrive, you need to either attach the harddrive to your pc(Quite a chore), or, I believe there is a homebrew app to rip the game from a DVD/CD and put it on the HD directly. I believe you can also somehow transfer ISO files over using yet another PS2 homebrew. But I could be wrong, I've not yet tried, so I'm only going off what I 'think' I've seen or heard.

And no, sadly, you will NOT be able to play PS1 backups. You can still play the original CDs of course, but no backups. Something to do with how the system checks the CD or something -shrug-.
However, I think someone was working on a PS1 emulator for the PS2(A little redundant, isn't it? Jeez). But I'm not sure how buggy or good it is.



Anyway, yeah. If anyone wants a memorycard modded, let me know and I'll PM you my address.
I would prefer if the memorycard was completely empty, but it doesn't need to be(Just a little more work on my end, no biggie). You do need to make sure you have plenty of space on the card though, just in case. If somehow you don't have enough space and you send me your memorycard, I'll rip a save or two off it(As in, rip it to a file using homebrew, like backing it up) and I'll send you the saves when you get your memorycard back and tell you how to put it back on.


But yeah, just putting this out there.

Also, not so tl;dr, tl;dr version: You can 'temporarily' mod your PS2 by putting a application on your Memorycard, that loads up on PS2 bootup. The application 'replaces' your System Menu with a Loader, to load other homebrews, just like the Homebrew Channel on the Wii.
PS2 Homebrew offers Emulators, Backup Loaders(No PS1 Support, sorry), and some other stuff I haven't looked into.
Putting the Loader on your Memorycard is harmless and it will not effect the PS2 itself. If you take the memorycard out, your PS2 will act like a normal, unmodded PS2 again.
You can, of course, still use the memorycard like you normally would if it's modded. You can still store gamesaves on it like normal. The app only takes up a tad bit of space.
When you have the application on your memorycard(Like I do), sending it to someone elses memorycard is 'extremely' easy. On the other hand, modding your memorycard from the beginning can be painfully hard. So if you want your PS2 modded, pay for the shipping here and back(I'm in Oregon, USA) and I will mod your memorycard and send it back to you.
Alot more details in the entire post above.