。
I was stuck with no way to keep the conversation going.
Literal
Conversation [gen-の] graft [subject-が] not-existing [and-て] was-troubled.
接ぎ穂 here is metaphorical, taking the horticultural sense (a cutting grafted onto rootstock) and extending it to a 'grafting point' for conversation — something to latch onto so the dialogue can continue. JMDict lists this as a distinct sense. なくて is the て-form of ない, chaining the cause to 困った ('was troubled'). The speaker is omitted — Japanese rarely restates the 'I' that English forces in.