Matt, assuming that the collapsed ceiling was caused by a defective condition preventable by the landlord (as opposed to an upstairs neighbor's overflowing bath), I believe your landlord is liable. Here is an excerpt of the applicable law:
RCW 59.18.060
The landlord will at all times during the tenancy keep the premises fit for human habitation, and shall in particular:
(1) Maintain the premises to substantially comply with any applicable code, statute, ordinance, or regulation governing their maintenance or operation, which the legislative body enacting the applicable code, statute, ordinance or regulation could enforce as to the premises rented if such condition substantially endangers or impairs the health or safety of the tenant;
(2) Maintain the roofs, floors, walls, chimneys, fireplaces, foundations, and all other structural components in reasonably good repair so as to be usable and capable of resisting any and all normal forces and loads to which they may be subjected;
Further, under RCW 59.18.230, if your lease or rental agreement contains a term waiving your rights under RCW Chapter 59.18, such waiver is prohibited and unenforceable.
Here's a link to the full chapter:
http://apps.leg.wa.gov/RCW/default.aspx?cite=59.18
Whether you can collect or not is another matter, but you may wish to write a letter to your landlord citing the law, and attaching an estimate for repairing the laptop (or a receipt, if you've gone ahead with the repair). Also include any photos, and include the costs of any other damage caused by the collapsed ceiling.
If the letter doesn't work, then you may bring such a claim to small claims court. I believe the damage limit for small claims is $3000 in Washington (this entire answer assumes you are in Washington). The Washington courts' site has a great self-help guide for small claims court. Here's a link:
http://www.courts.wa.gov/newsinfo/resources/?altMenu=smal&fa=newsinfo_jury.scc
Good luck!