I put a new battery cable on, sometimes I have to move starter cable to start car. What could be the problem?

check for battery voltage at the battery starter cable with starter switch engaged , if voltage is ok starter at fault, if no voltage solenoid or cable at fault.

If you get power by moving the battery terminals there is a loose or dirty connection, if the terminals on the cables are made of lead scrape them till they are a silver colour, same for battery posts .As a skin can form on the terminals and battery posts and make a bad connection , then check the other ends of the cables for tightness one cable will connect to the starter, the other to the chassie .

The following assumes that you get a 'click' when trying the starter. You need at test light or meter to troubleshoot--put the test light (meter) on the starter motor terminal, and have someone try the starter. If it turns on the light, the starter motor itself is bad. If no light comes on, then move the test point to the battery cable side of the solenoid and try for start again. If the light came on at first, but went out, check the positive battery cable connection at the battery--it may have corroded the copper wire inside the cable at the terminal or the terminal connection to the battery may need to be cleaned. If the light at the solenoid stayed on, then the starter solenoid is defective--replace it. Hope this helps!

Check the battery cables for corrosion near the battery terminal end. Sometimes it builds up under the rubber insulation. I would check the ground wire that runs from the battery to the engine block.

Neutral safety switch,starter relay, and check battery cables.

sounds like this is the starter relay the starter its self not working right or a bad battery lead check all are tight and clean first

with a new starter, this sounds like a bad battery cable or terminal end. the easier way to figure this out w/out checking the voltage drop across a whole battery cable is to affix the jumper cables strategically to find the bad one. Put jumper (+) on batt (+) and jumper (-) directly onto a piece of unpainted engine metal and not in the way of moving parts. If it starts this way then you've got a bad ground cable. If it didn't start, put jumper (+) on the hot post of the starter solenoid (there are 2 posts, only touch the one w/ the fatter cable going to it) or on a remote jump point if equipped, and put jumper (-) to batt (-). If it now starts you need a positive battery cable, or just a battery-to-starter cable (if separate)

disconnect and clean with baking soda and water solution, cable could be corroded inside, must be replaced, start early sat morning with new cable in hand 

look for the selenoyd conection or the starter Relay, also make sure that your battery terminals are clean, make sure You have connected the cable that goes to the battery to the right place

I would bet you are moving the positive battery cable? Here is the possible problem.......... The positive cable hooks to the battery terminal on one end and to the starter on the other. The one end to the starter is bolted on by one bolt. This does sometime get loose and all you have to do is take a wrench and tighten it. Now if this is not the problem the Battery cable may have sever corrosion inside the installation and when you bend it or move it about it starts working (just replace the whole cable). Either way it is a simple fix and easy on the wallet.