System will not power up

Go to this link and get one http://www.ebay.com/itm/New-250W-ATX-Power-supply-HP-Compaq-5187-1098-/360389017209?pt=PCA_UPS&hash=item53e8dbfe79

The green light flashing is a diagnostic LED light, telling you there is a power failure.
More specifically a bad Power Supply.
Weak voltage power rail.

The Power Supply used in a Compaq Presario SR1010Z desktop computer, is a 300 Watt unit, and is an ATX form factor.

[ATX form factor for a Power Supply, denotes the size of the Power Supply case, and the shape.
It is approximately 6 inches Long, 6 inches Wide, and 3-1/2 inches Tall.
The ATX form factor for a Power Supply is used in over 90 percent of the personal computers out there, and is as readily available as the air we breathe]

Usually, HP uses one of three generic Power Supply manufacturers.
1) Bestec
2) Delta
3) HiPro

All are low quality Power Supply manufacturers.

This is HP Support, and the main menu page for the Compaq Presario SR1010Z desktop computer,

http://h10025.www1.hp.com/ewfrf/wc/product?product=1146324&lc=en&cc=us&dlc=en&submit.y=7&submit.x=6&lang=en&cc=us

If you click on Manuals, then on Upgrading and Servicing Guide on the following page, there are instructions on how to open your computer case.

This is instructions on how to replace a Power Supply, from HP Support,

http://h10025.www1.hp.com/ewfrf/wc/document?docname=c01356113&cc=us&lc=en&dlc=en&product=3548196

(It's for a Pavilion a6230n desktop computer, but after you open the computer case of your Compaq Presario SR1010Z, the instructions are the same)

What Power Supply would I recommend?
There are 100's to chose from.
This is but one example,

http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=3276575&CatId=1078

Chosen because;

1) Maximum wattage is rated at 450 Watts.

A computer ONLY uses the power it needs, and NO more.
Wouldn't matter if you had a 10,000 Watt power supply, (No such thing. An exaggeration), if your computer only needs 100 Watts, it would only use 100 Watts.
(Surfing the internet typically uses 100 watts)

2) Has all the power cables you'll need, and more. Tie up the power cables you do not need. (Use plastic ties, Not wire, or bread wrapper ties)

3) 24 Amperes (24A) on the 12 volt power rail.

4) 135mm cooling fan.
The cooling fan on the Power Supply you have now is 80mm.

A larger fan turns slower. Produces as much air as a smaller fan, (Or more), but makes less noise.
Less wear on the fan's bearings also.

5) Is an ATX form factor Power Supply.

6) It's 80 percent efficient, compared to the 60 percent efficient Power Supply you have now.
(That is, if it was working)

do power flee

Chances are that 250w power supply is not going to power a motherboard with a 24 pin connector, but you can try.
You will need to purchase a 20 to 24 pin adapter cable.
Google Search Terms: 20 to 24 pin adapter

Technical Details

• Samsung Spinpoint HD103UJ 1 Terabyte SATA/300 Hard Drive General Features:
• 1 Terabyte formatted capacity 7200 RPM spindle speed SATA/300 interface 32 MB buffer
• 8.9 ms average seek time 4.17 ms average latency 3.5-inch form factor
• Improved recording stability over temperature with PMR
• Advanced dynamic FOD control for best data integrity

SATA Power3 Peripheral4 Floppy5 02 +3.3V (Orange)
03 COM (Black)
04 +5V (Red)
05 COM (Black)
06 +5V (Red)
07 COM (Black)
08 PG (Gray)
09 +5VSB (Purple)
10 +12V (White)
11 +12V (White)
12 +3.3V (Orange)
13 +3.3V (Orange)
14 -12V (Blue)
15 COM (Black)
16 PS-ON (Green)
17 COM (Black)
18 COM (Black)
19 COM (Black)
20 Blank
21 +5V (Red)
22 +5V (Red)
23 +5V (Red)
24 COM (Black)', CAPTION, 'Pin Signal (Color)', WIDTH, 150, BGCOLOR, '#000000', FGCOLOR, '#FFFFFF');" onmouseout="return nd();" href="javascript:void(0);"> This ATX12V power supply is a 300W, five output unit with remote on/off, and UL, CSA, and TUV approvals. RoHS compliant. Original HP part number 5188-2625 used in many Media Center, Pavilion, and Presario computers. Also serves as upgrade for HP/Compaq part numbers 5189-3964, 5188-0131, 5187-5116, 5187-6114, 5188-0129, and 410507-001. Airflow drawn out of case into surroundings by 80mm internal fan. Built-in power status LED above AC inlent. 2 x 12 (24 pin) main board power connector. Includes two daisy chained Serial ATA connectors. Bestec model ATX-300-12Z CDR, also replaces ATX-300-12Z BC, ATX-300-12Z BD, and ATX-300-12Z CC. i trust this helps

Do you mean the CMOS battery? (The little round one on the motherboard?)
In this case, you can replace the battery with a standard CR2032 lithium battery (3 volt, 220mAH rating). You get that at Walgreens, Radio Shack etc.
For how to replace the battery, take look at page 9 of the manual.
If you don't have one, you can download it here.

If you are looking for another battery, just come back here and leave a comment. I will check back and be happy to help.

it is your power supply it needs to be replaced

If the system recovery disk doesn't work it usually mans that the hard drive is bad. I would change the hard drive and use the system recovery disk on it after replacement. 

Sounds like a blown fuse in the psu, replace the unit and you should be good to go.

Make sure that the power button is conected to the right prongs on the mother board. On the writing next to the prongs it should say power.