I don't understand why people are asking about the CPU, it's stated in the first post that he has a Celeron. Most likely the dual-core Celeron (E1xxx series) which was launched in 2008.

That's a slow CPU by today's standards. Even internet browsing and MS office will feel laggy. A 2008-era PC will most likely have only 1GB or 2GB RAM, which isn't enough if you want smooth operation with Win 7.

Your 10k budget isn't enough for a decent gaming PC if you want to go brand new, but that's more than enough for a secondhand rig.

Get an i3 processor (i3-2100 or newer) and a decent video card (at least GTX 460). Pair those two with a true-rated PSU, 4 GB RAM and 1 TB HDD, and you'll have a PC that'll play DOTA2 with ease and will run fine for the next few years.