If you are not getting past the Windows Logo screen at this point I can only assume the following:
1.) Physical damage (Hard drive, Motherboard, Fan, Power Supply)
2.) Logical Damage (Boot Sector Virus, Root Kit, Bad Drivers, etc..)
Here are the steps (in order), I should/would take if the data on this system is critically important.
(Easy) = for the beginner, novice
(Hard) = for the beginner, novice
(Easy) (Physical damage) Check the CPU Fan. Is the Fan on the CPU running fast with no dust, dirt build up, or odd sounds - If the fan is not running at optimum it may be over heating the CPU causing it to fail. If it has been doing this for a while your CPU may be cooked. Cooked CPU = Time for new computer.
Clean your CPU Fan - http://www.youtube.com/watch?v=P0KNAel_X0Q&feature=related
(Hard) (Physical damage) Check the Power Supply Fan
Bad = Noisy, extremely dirty, not running. If it is dirty try to blow it out or have it replaced. "Caution" Do not try to remove and clean a power supply FAN, the capacitors in a power supply hold voltage even when they are turned off and could give you a poke you are not likely to forget.
(Easy) (Physical damage) Is it a bad Mother board check the capacitors - If you notice damage = Time for a New computer.
Good Capacitors are clean and flat on the top
Bad Capacitors are bloated even a little, corroded, discolored, burned, melted, or the contents are coming out the top.
Bad Capacitors - http://www.youtube.com/watch?v=HHTi4OcpGTk
(Hard) (Logical Damage) If everything so far checks out you may have (Logical damage) - A "good" tech could do this but unless this is free help you could spent as much as the system is worth having it done. This is usually done with a Boot CD or USB drive with testing software. The goal is to boot into an external Operating system and to interrogate the host Operating system to find common anomalies like (Boot Sector Virus, Root Kit, Bad Drivers, etc..). My experience is very few people have this skill-set, and are willing to take the time, because no one wants to pay for the time it takes to do it. If it takes 5 hours to test at $80 per hour = $400 or a new PC.
(Hard) (Logical Damage) Install new drive and reload everything from scratch, and install old drive as a second drive and copy the data you need off the old drive.
Replacing a hard drive - Watch this video - http://www.youtube.com/watch?v=vnEga6ga5hM
(Easy) Pay someone (local IT person) to backup data and repair current drive/PC
Hope this helps!