kenbaiki no mae de saihu wo sagasite itara, densya ga hassyasuru tokorodatta.

Here, 〜ていたら means something like while I was doing X or when I was doing X.

So:

• 財布を探していた = I was looking for my wallet
• 財布を探していたら = while I was looking for my wallet / when I was looking for my wallet

This たら does not always mean a deliberate if in the English sense. In sentences like this, it often introduces a situation that led to a discovery or another event.

A rough pattern is:

• 〜していたら、… = while I was doing …, … happened / I noticed …

So the sentence suggests that during the action of searching for the wallet, the speaker realized the train was about to leave.

Because 探していたら emphasizes an ongoing action:

• 探したら = if/when I looked for it or after I looked for it
• 探していたら = while I was looking for it

In this sentence, the speaker is in the middle of searching for the wallet at the ticket machine. That ongoing action is important because the next event happens during that time.

So:

• 財布を探したら、電車が… would sound more like when I looked for my wallet, ...
• 財布を探していたら、電車が… more naturally means while I was searching for my wallet, ...

Because で marks the place where an action happens.

• 券売機の前で = in front of the ticket machine as the location of the action 探していた
• 券売機の前に would focus more on being/existing/going to that place

Compare:

• 券売機の前で財布を探す = search for a wallet in front of the ticket machine
• 券売機の前にいる = be in front of the ticket machine
• 券売機の前に行く = go to the front of the ticket machine

Since 探す is an action, で is the natural choice.

券売機 means ticket vending machine and 前 means front or in front.

So:

• 券売機の前 = the area in front of the ticket machine

The の links the two nouns:

• A の B = B of A / B related to A

So literally, it is the front of the ticket machine, but in natural English it becomes in front of the ticket machine when combined with で.

Because Japanese often omits the subject when it is clear from context.

In this sentence, the speaker is the one searching for the wallet, so I is understood automatically:

• (私は) 財布を探していたら、…

Japanese leaves out things that do not need to be repeated. This is very normal and very common.

You could add 私は for emphasis or contrast, but it is not necessary.

Because 財布 is the object being searched for, so it takes を.

• 財布を探す = to look for a wallet
• を marks the direct object

The speaker is doing the action of searching, and wallet is the thing being searched for.

Using が here would be ungrammatical.

It means was just about to depart or was at the point of departing.

Breakdown:

• 発車する = to depart (used for trains, buses, etc.)
• ところ = point / moment / stage
• だった = past form of だ

So:

• 発車するところ = the moment when it is about to depart
• 発車するところだった = it was just about to depart

This pattern is very useful:

• V-る ところ = about to do
• V-ている ところ = in the middle of doing
• V-た ところ = just did

Examples:

• 出かけるところ = about to go out
• 食べているところ = in the middle of eating
• 着いたところ = just arrived

Because the train had not departed yet at that moment. It was about to.

These forms show different timing:

• 発車するところだった = it was about to depart
• 発車しているところだった = it was in the middle of departing
• 発車したところだった = it had just departed

So the sentence describes a near-miss situation: while the speaker was searching for the wallet, the train was right on the verge of leaving.

Because 電車 is the subject of 発車する.

• 電車が発車する = the train departs / is departing

In the second clause, the main event being described is the train’s departure status, so 電車 is marked with が.

This is especially natural when introducing or identifying what was in that state:

• 電車が発車するところだった = the train was about to depart

Both can mean something close to the train was about to leave, but the nuance is a little different.

• 発車するところだった focuses on the train being at that exact stage or moment right before departure.
• 発車しそうだった means looked like it was going to depart soon or seemed about to depart.

So ところだった feels more precise and tied to the actual timing. It strongly suggests the train was literally at the departure point.

In this sentence, ところだった is a very natural choice because it creates a vivid I almost missed it feeling.

Because this is casual/plain narrative style.

• 発車するところだった = plain
• 発車するところでした = polite

Both are grammatically fine. The plain form is often used in:

• casual conversation
• written narration
• diary-style storytelling
• examples in textbooks

If you wanted to say it politely, you could say:

• 券売機の前で財布を探していたら、電車が発車するところでした。

Yes. In Japanese, possession is often omitted when it is obvious from context.

So 財布を探していた naturally means:

• I was looking for my wallet

Japanese does not always say:

• 私の財布

because that would often be unnecessary. Since the speaker is the one searching for a wallet, listeners normally assume it is the speaker’s own wallet unless context suggests otherwise.

No. たら here does not express cause in that sense.

It links the two events in time:

• while I was searching for my wallet
• I found myself in the situation where the train was about to leave

So the meaning is not:

• because I searched for my wallet, the train was about to depart

It is more like:

• when/while I was searching for my wallet, I noticed the train was about to depart

In many cases, 〜たら can mean:

• if
• when
• once
• and then, as a result, I found...

The exact meaning depends on context. Here it is clearly the when/while type.

It breaks down like this:

• 券売機の前で = in front of the ticket machine
• 財布を探していたら = while I was looking for my wallet
• 電車が = the train
• 発車するところだった = was just about to depart

So the pattern is:

• [place] で [ongoing action] ていたら、[something] が [state/event] ところだった

It tells a short scene in sequence:

1. the speaker was in front of the ticket machine
2. the speaker was searching for a wallet
3. during that time, the train was on the verge of departure

Yes, it is natural.

It sounds like a normal narrative sentence describing a situation at a station. The combination of:

• 券売機の前で
• 財布を探していたら
• 電車が発車するところだった

works well and clearly communicates a realistic scene.

Depending on context, a native speaker might also say similar things like:

• 券売機の前で財布を探していたら、電車が出るところだった。
• 券売機の前で財布を探していたら、電車がもう発車するところだった。

But the original sentence is perfectly natural.