Hello and Welcome
This is what your eMachines T2862 is made of:
Specifications
CPU: Intel® Celeron® D 330 Processor
Operates at 2.66GHz
256KB L2 cache & 533MHz FSB
Operating System: Genuine Microsoft® Windows® XP Home
Chipset: Intel® 845GV chipset
Memory: 256MB DDR (PC 2700)
Expandable to 2GB
Hard Drive: 60GB HDD
Optical Drive: 48x Max. CD-RW/DVD Combo Drive
Media Reader: 8-in-1 digital media manager (USB 2.0, Secure Digital™ (SD), Smart Media, Compact Flash, Memory Stick®, Memory Stick PRO, Micro Drive, Multimedia Card)
Video: Intel® Extreme Graphics 3D
64MB Shared memory
Sound: AC '97 Audio
Sounds like XP Home is corrupt, or the hard drive is dieing... It is also very possible that the system is past it's useful life, and it will need a new power supply and motherboard soon. It can be totally rebuilt for around $200 if need be, or you can save for a new system