For sure your partitioning is wrong.
The first partition needs to be a small 100MB to 300MB size, formatted fat32, flagged boot.
Used as boot partition, with all the boot loader files on it.
The two other partitions seem OK, but what format are they?
Make a 4rth partition as the swap partition.
To give you more advice we really need this information:
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Usually for duel installs with other Linux OS's.
Install the other OS first.
Then install Puppy Linux.
Then install the boot loader to boot both of them.
Grub4dos is good at making boot loader menu entries for other Linux OS's, if it finds them installed on the drive.
But there are so many Linux OS's, that it may not make one.
You may need to manually make the menu entry.