You can check with local PC repair shops, let them know to call you if they get hold of an old PC. These 386, 486, P1, P2's are not going to be in stock at most shops, they can't make money on them. Yard sales will always find you an older PC. Even flea markets I've gone to have a few vendors with them.
eBay is your best bet. The last few yrs I've seen the amt of older PC's become quite small and many no longer are in very good shape, broken hinges, missing parts, etc... If you are patient and willing to buy something other than a Toshiba you'll find a good condition laptop. Took me two weeks of searching numerous times a day to find an almost mint condition PC that will run DOS and scanners well
Also ask relatives and neighbors if they have or know someone who has an old PC. I found several this way. You might want to look into the error msg you get on your PC, maybe you can just reload the OS to fix it. If it's hardware then you have a whole 'nother issue to deal with.
This is "sick" -
Working Toshiba T1910 Antique Computer/ Laptop | eBay He wants $1000 for the same PC you have! Gotta be a typo!
Toshiba Satellite T1960CT 486 laptop computer | eBay Is this one any good to U? Still quite pricey for a 486 PC but he has a Best Offer option. Look at Micron, Gateway, Libretto, HP, Compaq for older PC's. There were a bunch of laptops made back in the day that had slow processors. eBay has tons of them but you need to use the right search parameters to find them.
Check your township and County recycle centers to see if they will allow you access to the recycled PC's they've taken in. There are also a few "Green" PC recycle stores on the Web, you might get lucky.