he offered to let him play with hem,(but)the boy said

说白了,这涉及到英语的基本结构,两个单独的英语句子不可以简单的用逗号连接,要么中间加并列连词变成并列句,要么把其中一个变成从句.如：
He was ill,he didn't go to school.是错的.可以改成：
He was ill,so/and he didn't go to school.
或者Because he was ill,he didn't go to school.
回到你的句子,but是并列连词可以用,then是副词不能用.
其实,还有一种办法解决要用到非谓语或独立主格,这要麻烦些,自己先看看再说.