Wow, I saw one of these parted out recently because the 'screen stopped working'. It's just some electrolyte eating up the traces.
You will need to buy some new caps that match the specs of your original ones that have leaked. Replacing just the ones that have leaked should be fine, those are usually the ones that got pushed the hardest - I did a similar repair with my T1950CT's DC-DC converter board. I took off every single cap and tested them, only one cap (C511) was bad. After replacing that it's all up to working again: Re: Toshiba T1910
Here's a really good visual for a safe way to remove caps from a PCB without damaging the PCB traces / pads: https://twitter.com/TubeTimeUS/status/1440865127713021956 (wow those are some awesome looking side cutters)
The repair gets much much harder if the pads or traces get lifted.
Once the caps and their legs are removed, clean up the electrolyte with IPA. Then put some kitchen roll on the PCB and brush that onto the IPA to really clean it up.
The electrolyte can flow around sometimes so do check to see how far it may have travelled. Toshibas from around this time use a lot of flux which can look pretty gnarly when you partially clean it with IPA, but flux on a board should be fine.
It looks like the corrosion may be under some of the solder mask on a couple of those traces, see if the solder mask comes off easily and ensure the copper traces look good. They can be resealed with nail varnish / UV solder mask.
For the replacement caps, anything of matching spec should be fine. Especially if like my computers, it's just for occasional use. I would go with 105C rated caps though, since it's easy to tell the voltage / capacitance of a cap, less easy to tell the thermal rating on SMD caps like thes in your picture. You can use regular through hole capacitors in place of the SMD caps, just bend their legs around as long as the case still fits together.
