Don't install EasyOS to your hard-drive until Barry K confirms that the following will not take place.
When you use dd to install EasyOS to a USB-Key initially it writes only a 639 Mb +/- vfat partition. That partition contains its boot-loader and the base EasyOS system. The first time you boot up that EasyOS, however, it formats the rest of the USB-Key creating a 2nd Linux Ext4 partition and, obviously, wiping out anything which might have been in that space.
I assume that won't happen if you merely copy the EasyOS files from a USB-Key to a hard-drive. But that's a guess. And, merely copying those files doesn't include a boot-loader which would enable you to boot into it. That's part of the problem I sought an answer to in these posts. viewtopic.php?p=21985#p21985 and viewtopic.php?p=22259#p22259
Always try operating systems from a USB-Key first. If you can't boot into it from a Key, It's unlikely you will be able to boot into it from the hard-drive. And, even if it boot up, you want to be sure that important system --like keyboards, your monitor and wifi-- are fully functional.
Find a Puppy which does work with your computer. Puppys are modular. With Puppys built in the last 5 or 6 years, you can always 'swap kernels'. A Puppy's kernel consists of two or three files(systems): vmlinuz, a zdrv.sfs and sometimes an fdrv.sfs. (Sometimes the fdrv.sfs containing firmware is required. Other times the zdrv.sfs includes both drivers and firmware. Adding unnecessary fdrv.sfs doesn't hurt: it just includes firmware you didn't need). To swap kernels you just have to swap the vmlinuz, and swap and rename the zdrv (and maybe fdrv) renaming it/them to that used by a particular Puppy: e.g., Fossapup64's main SFS is named puppy_fossapup64_9.5.sfs; its zdrv.sfs is named zdrv_fossapup64_9.5.sfs.
But EasyOS is not as modular. I'm not sure where it's located drivers and firmware or if it would recognize (load on bootup) a zdrv or an fdrv or if loading either would break something.