I also have the old TomTom ONE v1, 3.5 inch screen with 32Mb RAM and only an SD card slot, no internal memory. I have it working superfast, even better than it was straight out of the box. You don't need a new device if your ONE is just running slow. You just need the right navcore that works well with your model.
I've tried tons of navcores, nearly all 8xxx and 9xxx versions many times. I have found the 8.562 SE to be the most compatible and the fastest of the lot. Trust me, you won't be disappointed. I get 8Mb free RAM when booting the device and everything runs smoothly. Everything including the menu buttons and recalculating works faster than ever before.
All you need is:
1) A full current backup of your device
2) 8.562 SE navcore
3) The latest full featured 865_3245 map for your country
4) FastActivate Premium Edition (latest version)