Dropped MacBook broken screen can't read serial number for support. External monitor blank but shows cursor.

You may be able to see the booted computer's desktop Finder and access

the serial number and other details, by trying some options mentioned here,

and note comments, as details are hashed out there by original interaction.

If you have the correct adapter for use with external display, the means to

use the display with the MacBook and make the external screen appear in

full size, helps be able to look into the system "About this Mac" for serial #.

http://ask.metafilter.com/208526/help-me-boot-my-macbook-with-a-dead-screen-to-a n-external-monitor

This other page has several items, and perhaps number 4 may work to see

the external display, after startup, attach the display close the lid and then

wake it up by touching any key (or read other ideas to see what/if any works)

http://livingdigitally.net/2006/10/02/using_an_extern/

{The lid would probably have to be closed at some point in the pre-boot cycle

to be able to force the computer to use the external display, after choosing

keyboard shortcuts; as suggested in article link above. There may be others

so if those do not work after trying several times, carefully search online.}

There are links within the main Contact (or in the Apple Support) pages that

could be helpful to see the level of support, service, and repair that may be

available to you and your product. Depending on vintage, or if the unit is not

too old for someone at the Apple Store or their repair facilities to fix issues,

they could. The official Apple store also, depending on location, offers Genius

staff (appointments, set ahead, are preferred to walking in & waiting around)

to help you with product issues, diagnostic, and recommendations for service.

• MacBook - Contact Support - Apple support:

http://www.apple.com/support/macbook/contact/

(there is another section for MacBook/Pro, & others as well)

Older products no longer handled by Apple, would usually be referred to the

knowledgeable Apple authorized service providers in the area who can fix

them; some items may be harder to get parts for, and newer ones under the

Apple Care or initial complementary service/support are the Store's focus.

• See all worldwide support telephone numbers
• Find an Apple Authorized Service Provider
• Visit an Apple Retail Store
• Check your repair status

If you are not in the US or where there is an online Apple Store or local one

you know of, you can use the online Locate pages to see who what where

regarding diagnostic, testing, estimates, availability of parts, & if the work is

something they'd do in the retail official store repair facilities.

So because there are so many different MacBook models including the newest

12-inch Retina MacBook, various MacBook/Air, MacBook/Pro and older MacBook

models with a variety of display sizes, processor types, & other configurations, an

item would be best identified to the store or authorized service provider by serial

number, model build number (example MacBook5.1, etc) and build year.

The everymac.com site has much information on many models & specifications.

Also the ifixit.com site has repair guides for mac models, including portables.

The earlier MacBook models from 2006 toward 2010, some of them have a user

removable battery and some of those have the serial number visible beneath it.

• How to identify MacBook models - Apple Support

• How to find the serial number of your MacBook/Pro - Apple Support

There also are some numbers in small nearly illegible print on the case near hinge

area, sometimes a serial number. Or a model number that may cover several year

builds; not a true identifier. -- To identify the unit by obvious information also helps.

The size of the display, and other things you know to be true; original packaging helps.

Or online in section where you see your products SNs, even after Applecare expired.

Good luck in this matter! 🙂