You should have tested it before buying it if you don't know how to fix it.
It could be anything from a fuse to something much worse. Electrical/mechanical parts should be easy to find.
Where are you located?

Transformers rarely fail.
I have a friend out your way who services games. I'll contact him, and see if he might come out to help you.
He will likely charge you, but I'll have him contact you first. PM me with your contact information.

The coil on the coin door is not needed for home use. It's purpose is to return a coin inserted into the game when it's turned off. You can snip the wires leading to it, and wrap the wire ends with electrical tape. You can get this coil,and just about every other electrical and mechanical part from Pinball Resource (pbresource.com).
If you call there and talk to Steve, tell him you're a newbie. As was mentioned above, he does want part numbers when you order parts.
Is this the same "Golden Arrow" that was listed on eBay recently? The playfield on that one had a tremendous amount of wear.

I guess not. It's still listed.

It's great that the game came with a manual and schematic. The only broken plastic parts that Pinball Resource won't have are the lightshield plastics. They are the flat plastic parts with game specific artwork that cover the triangular lower slingshots and other areas. The pop bumper cap and lane guides are available.
The star cap part number is A-16838 (specify red star). You should get both so that they match. The "100 POINTS WHEN LIT" cap is also available. Here's a link to the page. http://www.pbresource.com/pfbumper.htm
The game is pretty rough cosmetically; even the backglass isn't very good (faded as well), but it's your first pin. Educate yourself, get it working and enjoy it for what it is. Read Clay's repair guide, and you will have a good general idea of how to get started.
I once got a "Golden Arrow" on eBay that was a mess, but it was a diamond in the rough. It had many issues which the newbie might have had difficulty with, but the game came out looking and playing like new. Don't get discouraged. You have help here and check out this thread: https://pinside.com/pinball/forum/topic/a-275-el-doh-rah-no/page/2#post-4559509. Many games have been saved by dedicated guys like him. Your game needs a little work, but it should be
fairly easy to get it playing again. Good luck.

Nice! Didn't know they redid "Golden Arrow" plastics.

Read my post (#11) above. That coil is not needed, but you can get a replacement from Pinball Resource if you want.

As Black_Knight mentioned above, open the backbox and manually click the credit wheel up several notches to add credits. The photo you posted shows the wheel at zero, so if the game isn't jumpered for free-play, it won't start at zero.
And, as jeffc says, lift the playfield, and with the game switched on, manually nudge the motor counter-clockwise. It should rotate 1/3 of a revolution then stop.
The normal condition when the game is switched on is "tilt". Of course you should have checked all the fuses by now (unplug the machine first), and verify their proper value.

I believe this is the third time this has been asked, but we still don't know.