That laptop tilts things toward the replace laptop scenario. It is the same laptop as the hp/compaq presario cq61. Here are the instructions for replacing the laptop fan and replacing the thermal paste used to ensure heat transfer.
How to disassemble Compaq CQ61 - pc-level.com
This model is one where you have to disassemble the entire laptop since the fan and heatpipe assembly are between the motherboard and the plastic base.
The hard drive should be tested using the utility that comes up when you tap the f2 key when the bios /hp logo first appears. It is quick so keep tapping the f2 key while doing the power on. If you miss it tell windows to restart and keep tapping the f2 key until you get in.
Run the drive diagnostics and note any error codes.
Software wise, malware can cause slow boot and downloading malwarebytes antimalware from
Malwarebytes : Free anti-malware download can find most malware that can slip behind commercial popular antivirus programs.
Hp makes some easy to repair laptops and most of them can be found by searching for "HP Business Line Probook"
My hp 4530s has one screw that locks the entire back in place so I can pop it off and replace ram, wifi, drives or fan assembly in minutes.
You do not have to spend more than 400 to 700 on a laptop to get a good one. It would take me probably 3 hours to replace parts on your laptop even if we knew all the parts that need replacing. In a commercial environment (a shop) this would surely exceed the value of the current laptop and probably exceed the cost of the lower end new laptops from HP/Compaq, Lenovo or Toshiba. If you were closer to Seattle I could fix it for free if you are on a fixed income or on a sliding scale based on your income. I even have a cq61 in the dead laptops pile here in my store room.
If the power button is failing then that may also indicate a problem that needs a major part replaced. (motherboard)
For reference, here is the service manual for this laptop. You may find someone near you who could repair your laptop using this reference.
http://bizsupport1.austin.hp.com/bc/docs/support/SupportManual/c01740724/c01740724.pdf
good luck
