My own first computer-like thing was a homebuilt "adder" using discrete 7400 TTL chips (AND, OR gates, and a latch).
It had 4 toggle switches, 2 push buttons, and 5 transistors driving 5 light bulbs. (And cost me probably $120)
It worked like this:
Power on, reset.
Press one button to enter a number,
enter 4 binary digits on the toggles for first number,
press the button again to enter second number,
enter 4 binary digits on the toggles for second number, and
press the button again to add and show result.
Then the light bulbs would light the resulting binary value.
(And the geeky trivia question: why were there FIVE light bulbs instead of four?)
It's a shame nobody answered this yet. I suppose I'll do it then, it's not like I've got something better to do ATM

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You need the extra lamp to display results bigger than 1111. The biggest value you can make with 4 bits is 1111 (15). If you add 2 4-bit numbers, then you can get a maximum of 11110 (30). So 5 lamps are needed.
"My" first computer was a 186 or 086 (not sure any more), we got it second hand. Me and my little brother really wanted some gamesystem, but instead my parents got us a real computer. I sure spent a lot of time playing those classic games. Just boot from a floppy, and start the gaming fun.
Since then our family had a couple of computers, the only one we bought new was a 486-DX2 (66 MHZ, with a 2 speed cdrom drive, a soundblaster pro {8 bit} soundcard, and I think it had a modem too). It was at the beginning of the windows 95 era but ours still had dos + windows 3.11. Even then it was nice to be able not to boot into Windows and use resources for the programs you really wanted to play

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Since then I bought only laptops, on the first one (a second hand Compaq Armada m300, p2 300) I meant just to make music in Fasttracker II (which also ran great on my old 486!), but I soon started using it for other things too. Thus my love for laptops was born. I bought the same but slightly newer and improved model (a p3 600) from a friend. Both these laptops are still in my posession and never really gave trouble.
The newer laptops I've owned so far have all had defects, and I don't wish to talk about the trouble I had with ASUS laptops and their customer service. My last ASUS laptop was stolen when we got burgled, so I bought the desktop replacement laptop in my signature. Never would've dreamed something like that could ever exist when I was playing Commander Keen on my old XT....