Cold car starts and sometimes doesn't?

I have a 1997 Honda Accord and just recently purchased it for a really cheap price I couldn't pass up so it has a problem when starting cold I tried to start it yesterday since it's been sitting for about a week without starting and I go to turn it on and it just cranks. It usually starts but this time a no If someone could give me some ideas on locating and narrowing the problem it would be awesome thank you.

Just a thought… The 1997 Honda has fuel injectors. Get a fuel injector cleaner (at the auto shop) and put in a full take of gas. (Put the cleaner in before you fill, as it helps to 'stir' it in.) This will clean them as well as helping the engine to start easier.

Other than that, I'd consider using a higher grade of gas for a tank or two, and finally, take it to a mechanic for a going over.

The most common problem is an intermitttent fuel pump relay, also known as the "main relay." Whacking the dash on the top of the passenger's side with your hand will often get it to make contact. If so, the relay has to be replaced. It's an easy DIY job except that you have to reach way up under the dash to do it.

Another possibility is a bad ignition switch. When you switch it into the "run" position the oil pressure, check engine lights, and battery warning should light. If not the ignition switch is bad. A medium DIY job and about $50 for the part. There's a recall on your 1997 Accord for the ignition switch (it can fail while driving, while the main relay rarely does). See the source.

Check the condition of your spark plugs (overly black and sooty)? How are the fuel injectors?

These cars were known for main relay issues as Flag Michael says. You can check for power and ground at the fuel pump while cranking with a test light if it does not start. If there's no power, it is likely a bad main relay. But before you get deep, replace the plugs, wires and air filter first and see if the issue goes away.

If it ever starts drive it to an auto parts store and ask them to run the codes. That will be the easiest way to find out what the problem is.

If it cranks and doesn't start it's either not getting spark or not getting gas.
1. Test the gas flow. Is it getting gas?:
- Have someone help you. One of you turn the key to the on position (without starting the vehicle) and the other person be as close to the gas tank as they can get. In the first second or two of the key being turned to the lock position just before the start position the person at the fuel tank should hear a buzzing noise, the fuel pump working. No noise? Fuel pump has failed.
- Check that the fuel line at the motor is getting flow sending it into the engine. Find the fuel line at the motor and disconnect it. Do the same as the above with the key. If there's no flow… It's not getting gas for some reason. If the fuel pump is working it's possibly due to a clog in the line which is most likely at the fuel filter. Follow the lines to find the fuel filter and replace it. They're cheap and pretty easy to replace just be careful with the fuel lines they can be quite brittle and kink very easily. You can test to see if the filter is clogged by blowing through it but I wouldn't recommend doing that because gas tastes disgusting and you're guaranteed to get a taste doing that.
Fuel filters have different locations however in most vehicles they're mounted somewhere near the middle of the fuel line along the frame rail. Some are located right at or after the fuel tank, some are located in the engine compartment at the end of the line just before the line sends fuel into the engine.

2. Test spark:
- Pull a spark plug out. Most pull cylinder #1 but it doesn't matter which one you pull at first to look at it. Regardless of their age they will be black and carboned. You're looking to make sure the gap between the post and needle that's through the center of the plug isn't touching. You're also visually inspecting them for gummy residue. If they're gummy, they're failing. Replace them.
**ONLY PULL ONE SPARK PLUG AT A TIME**
… If that's not the cause…
- Once pulled connect the spark plug to it's wire and while using channel locks with a rubber coating on the handles hold the spark plug's threads against something metal like the engine block or a bracket and have someone turn the key cranking the engine. You should see sparks tick ticking away as the engine cranks. No flash of spark? Something else is wrong. A car only has 12 volts which isn't very much but it is an uncomfortable shock if you end up getting zapped but some mechanics do this with their bare hands. I prefer no chance of getting zapped so I use channel locks or long pliers that have a rubber handle.
.
… Getting gas, but still no spark after checking and replacing all of the plugs and wires? If you replace the plugs you may as well replace the wires too.
- Find the starter. Follow the wires to where they go. Not the battery cables, the other wires to inspect them for breaks, bare spots where there's no insulation that could be shorting out, and nasty kinks in the wires that could be causing a short. Following the wires you'll find the coil pack. If everything else is good (you're getting gas and spark) that is the next thing I would replace. I'm personally not aware of or even if there's a way to test a coil pack. I just replace them if I question them.

It's not the battery because the engine is cranking. If there was a problem with the battery the engine would not crank. It's a spark or gas flow problem.

Check for spark
Check the fuel pressure
Check to see if the cam timing jumped.
Find a mechanic that knows how to check those things.