I'm probably stretching your definition of "computer" with this answer, but I personally still consider it a computer (A programmable device with microprocessor, memory, storage, input and output)...Texas Instruments TI-86 Graphing Calculator from 1996. Zilog Z80 6MHz, 96KB RAM, 128x64 monochrome LCD, TTL-compatible micro serial port, programmable with BASIC and Z80 assembly. I use it to calculate invoices for customer repair jobs when out in the field, wrote a custom program specifically for this purpose.
Or, depending on your definition of "use", I suppose you could also count the onboard computer that runs the electronics in my 2008 Buick LaCrosse. The car won't run without it, so in a sense I use it every day! 🤣
Beyond that, the oldest system that most everyone would accept in the scope of this thread is only a couple years old. Lenovo IdeaPad P400, Core i7-3632QM 2.2GHz, 8GB RAM, 1TB hard drive, DVD burner, wi-fi, 14in touchscreen, Windows 8.1, typical boring modern-day computer stuff. I use a couple slightly older Windows 7 systems at work, but since they're not "mine" proper as the OP originally stated, they don't count.