No one has any ideas?

The P7450 (or P7350, P7550, etc.) is compatible with your system.  The same goes for any P8x00/P9x00-series Core 2 Duo (P8400, P8600, P8700, P8800, P9500, etc).

The T7250 is the base model dual-core processor option on the E5400,  so it's certainly compatible also.  But the T7250 is based on the older 'Merom' architecture rather than the newer, faster, more efficient 'Penryn' architecture.  It will certainly outperform your current single-core Celeron, but the Penryn chips run rings around it!  I would skip it...

is intel T7200 processor compitable?

No. It's an older generation CPU.

Thanks very much, its older but has 4mb cache,

Hi there,

Do you know if the latitude e5400 is compatible with an Intel core2duo E8600 cpu or generally with the E8000 series? It is cheaper and faster than then P or T series but i can't find any info on compatibility.

Thanks in advance.

No.  The E-series processors are for desktops -- not notebooks.

OK many thanks for letting me know, you saved me some money on that!

What about the i5-580m processor then? It works on a latitude e6410, would it work on a latitude e5400?